Test #3
Let f(x)=sinx and g(x)=cosx.Find the value of (f•g) (π/4).
5.3 Q#9
Name the quadrant in which the angle θ lies.
5.4 Q#5
Is the tangent function even, odd, or neither? Is its graph symmetric? With respect to what?
5.5 Q#11
Solve the following triangle. A=20°, B=20°, c=2
7 Q#4
The point P=(4,−3) on the circle x^2+y^2=r^2 is also on the terminal side of an angle θ in standard position. Find sinθ, cosθ, tanθ, cscθ, secθ, and cotθ.
5.5 Q#2
What is the domain of the sine function?
5.5 Q#9
Find the exact value of the following expression. tan^-1 sqrt(3)/3
6.1 Q#1,2,3
Find the value of each of the six trigonometric functions of the angle θ in the figure. a=7 and b=6
5.2 Q#1,2
Given cos30°=sqrt(3)/2,use the trigonometric identities to find the exact value of each of the following. (a) sin60° (b) sin^2 30° (c) secπ/6 (d)csc π/3
5.2 Q#11,12
Find the distance from A to C across the gorge illustrated in the figure.
5.3 Q#11
For what numbers θ is f(θ)=tanθ not defined?
5.5 Q#13,14
Find the exact solution of the equation. 18sin^-1 x=3pi
6.1 Q#10
Find the exact value of the following expression. sin-1 (-sqrt(3)/2)
6.1 Q#11
Write the trigonometric expression as an algebraic expression in u.
6.2 Q#10,11
Use the half-angle formulas to find the exact value of the trigonometric function sin(-22.5)
6.6 Q#2,3
Establish the identity sin7θ+sin3θ / cos7θ+cos3θ =tan(5θ).
6.7 Q#4,7
Use the right triangle and the given information to solve the triangle. a=5, B=34°; find b,c, and A
7 Q#1
A tower.... A state trooper A aircraft
7 Q#11,12,13
Use identities to find the exact value of each of the four remaining trigonometric functions of the acute angle θ. sinθ = 1/5 , cosθ=2sqrt6/5
5.2 Q#3
Use the definition or identities to find the exact value of each of the remaining five trigonometric functions of the acute angle θ. sinθ= sqrt5/4
5.2 Q#4,5,6
Use fundamental identities and/or the complementary angle theorem to find the exact value of the expression. Do not use a calculator. sin19 csc19
5.2 Q#7,8,9,10
Find the exact value of the expression. Do not use a calculator. 8cos45-7sin45
5.3 Q#1,2,3,4
A right triangle has a hypotenuse of length 3 inches. If one angle is 38°,find the length of each leg.
5.3 Q#10
A right triangle contains a 75° angle. (a)If one leg has length 11 inches, what is the length of the hypotenuse? (b)There are two answers. How is this possible?
5.3 Q#12
Suppose you are headed toward a plateau 53m high. If the angle of elevation to the top of the plateau is 60°,how far are you from the base of the plateau?
5.3 Q#13
Use the reference angle to find the exact value of the following expression. Do not use a calculator. cos 420
5.4 Q#8,10
Use the reference angle to find the exact value of the given expression. sin(-120)
5.4 Q#9
Find the values of sin t, cos t, tan t, csc t, sec t, and cot t if P=(−1/2, sqrt(3)/2 is the point on the unit circle that corresponds to the real number t.
5.5 Q#1
Is the sine function even, odd, or neither? Is its graph symmetric? With respect to what?
5.5 Q#10
What is the range of the secant function?
5.5 Q#15
Use the fact that the trigonometric functions are periodic to find the exact value of the given expression. Do not use a calculator. sin(420)
5.5 Q#3,4,5
Use the even-odd properties of the trigonometric functions to find the exact value of the given expression. Do not use a calculator. cos(−60°)
5.5 Q#6,7,8,12
Find the exact value, if any, of the following composite function. Do not use a calculator. cos^-1 [cos(7pi/10)]
6.1 Q#6,7,8,9
Find the exact value of the expression. cos[sin^−1 (1/2)]
6.2 Q#1,2,3,4,5,6,7,8
Solve the equation. 2sin^2 θ-3sin θ + 1=0
6.3 Q#8
Two sides and an angle are given below. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any resulting triangle(s). a=8, c=6, C=10°
7 Q#5,6
Solve the triangle
7 Q#7,8,9,10
Develop a formula for cos(3θ) as a third-degree polynomial in the variable cosθ.
6.6 Q#4
Use the information given about the angle, 0≤θ<2π, to find the exact value of each trigonometric function. tanθ=−2, sinθ<0 (a) sin(2θ) (b) cos(2θ) (c) sinθ/2 (d) cosθ/2 (e) tan2θ (f)tanθ/2
6.6 Q#5
Find the exact value of each of the remaining trigonometric functions of θ. cosθ=−24/25, θ in Quadrant III
5.4 Q#11,12
Use a coterminal angle to find the exact value of the expression. Do not use a calculator. tan 405
5.4 Q#3,4
Find the reference angle of 130°.
5.4 Q#6,7
Find the exact value, if any, of the following composite function. Do not use a calculator. tan^-1 [tan(-5pi/17)]
6.1 Q#12,13
Use a calculator to find the value in radians of the following expression rounded to two decimal places. tan^-1 8
6.1 Q#4
Use a calculator to find the value of the following expression rounded to two decimal places. cos^-1 1/11
6.1 Q#5
Use a calculator to find the value of the expression rounded to two decimal places. cot^-1 (-sqrt(7))
6.2 Q#9
Use a calculator to find the approximate value of the expression. Round the answer to two decimal places. tan31
5.3 Q#5,6,7
Let f(x)=sinx and g(x)=cosx. Find the value of (f+g)(45°).
5.3 Q#8
A point on the terminal side of an angle θ in standard position is (−7, 24).Find the exact value of each of the six trigonometric functions of θ.
5.4 Q#1,2
Solve the equation on the interval 0 < θ <2pi. 4sin θ + 5 = 7
6.3 Q#1,2,3,4
Solve the equation. Give a general formula for all the solutions. List six solutions. sin θ = -(sqrt(2)/2)
6.3 Q#5
Solve the equation. Give a general formula for all the solutions. List all the solutions for k=0, 1, 2, 3, 4, and 5.
6.3 Q#6
Solve the equation on the interval 0≤θ<2π. sqrt2 sin^2 θ - sin θ=0
6.3 Q#7,9,10,11,12
Rewrite tanθ•cscθ in terms of sine and cosine.
6.4 Q#1
Rewrite (sin θ−cos θ) / sin θ − (sin θ+cos θ) / cos θ over a common denominator. Type your answer in terms of sine and/or cosine.
6.4 Q#2
Establish the identity. (1-cos θ)(1+ cos θ) = sin^2 θ
6.4 Q#3,4,5,7,8,9,10
Verify the identity. cosx − sin^2 x cosx = cos3x
6.4 Q#6
Use a sum or difference formula to find the exact value of the trigonometric function.
6.5 Q#
Establish the identity. sin(3pi/2 - θ) = -cosθ
6.5 Q#10
Find the exact value of the expression. sin(10) cos(20) + cos(10) sin (20)
6.5 Q#2,3,4,5,6,7
Find the exact value of each of the following under the given conditions below. tan α = −12/5, π/2<α<π; cosb.....
6.5 Q#8
If sinθ=4/9, θ in quadrant II, find the exact value of (a) cosθ (b) sinθ+π6 (c) cosθ−π3 (d) tan(θ+π/4)
6.5 Q#9
If sinθ= 40/41, 0<θ<π2, find the exact value of each of the following. (a) sin(2θ) (b) cos(2θ) (c) sin θ/2 (d) cos θ/2 (e) tan 2/θ (f) tan θ/2
6.6 Q#1
Express the given product as a sum containing only sines or cosines. sin(9θ) sin(7θ)
6.7 Q#1,2,5
Express the given sum or difference as a product of sines and/or cosines.
6.7 Q#3,6
Solve the triangle shown to the right.
7 Q#2,3
