trig unit 3
What is f*g if f(x)= 1/x+2 and g(x)=x^2?
1/x^2+2
The equation cos2x = 0 has 2 solutions on the interval [0, 2ππ)
False
The equation tan5x = -3 has no solutions
False
A boat is 75 miles west and 60 miles north from the nearest port. What bearing should be taken to sail directly to port?
S 51° E
Frequency and period of simple harmonic motion are reciprocals of each other
True
Inverse sine is an odd function
True
For h(x)=x^6+x^3, find f(x) and g(x) such that h(x)=g*f(x)
f(x)=x^2, g(x)=x^3-x
Solve the equation: 2 tan^2 (x)-18=0
x = ±arctan(3) + ππn, where n is an integer.
Find the solutions of the following equation: tanx = 0
x = ππn, where n is an integer
Evaluate f*f(2)
-2
What is arctan(-√3)
-60°
Find the exact value of cos75? + cos195?
-√6/2
Evaluate f*g(1)
0
What is the period, in seconds, of the simple harmonic motion described by the equation x = 5sin(8ππt)?
0.25
What is f*g if f(x)=1/x+2 and g(x)=x^2?
1/x^2+2
Write cos(arctan(x)) as an algebraic expression
1/√x^2+1
For f(x)=2/x-3, find f^1(x)
120°
A handicap-accessible entrance to a building is 6 feet above the ground and is connected to the ground level parking lot by a ramp. If the length of the ramp is 25 feet, what angle does the ramp make with the ground?
14°
Find the exact value of cos^-1(tan 135°)
180°
Find the exact value of sin (cos^-1(1/3))
2 √2/3
A plane is 180 miles south and 95 miles east of the airport. What bearing should be taken to fly directly to the airport?
332°
In an isosceles triangle, the equal sides are 10 and the altitude dropped to the base is 6. Find approximate degree measures of all the angles in the triangle
37°, 37°, 106°
n an isosceles triangle, the equal sides are 10 and the altitude dropped to the base is 6. Find approximate degree measures of all the angles in the triangle.
37°, 37°, 106°
Find all solutions of the following equation: tan(1/4x)=10
4arctan(10) + 4ππn, where n is an integer
Find a model for simple harmonic motion with amplitude 5 cm and period of 0.5 seconds, such that the displacement is 0 when t = 0
5sin(4ππt)
Angular frequency equals frequency divided by 2π2π
False
Arctan(tan(105°)) = 105°
False
Composition of secant and cosine is an identity
False
Functions f(x)=^4√x+3 and g(x)=(x-3)^4 are interses of each other
False
If in the equation tanx = a the value of a is negative, then x is also negative
False
Inverse cosine is an even function
False
Simple harmonic motion can be modeled by any periodic function
False
The arctangent function is a ratio of the arcsine function to the arccosine function
False
The composition functions f?g and g?f are equal to each other for any f and g
False
The domain inverse tangent is [−π2,π2]
False
The equation tan^2(x)-25=0 has 2 solutions on the interval [0,2π)
False
The function given as the following set of ordered pairs is invertible:{(-7, 1) ,(-3, 4), (1, 9), (5, 4) (9, -1)
False
The product of two sine functions equals the sine of the product
False
The range of inverse cosine includes some negative numbers
False
The sum of the cosines equals the cosine of the sum
False
Amplitude is the maximum displacement of the object in simple harmonic motion
True
Arccos(cos(-25°)) = 25°
True
Function f(x)=2 √x-3 +5 is invertible
True
If f(x) = x, then f?g = g?f for any g(x)
True
In a right triangle, it is sufficient to know the lengths of any two sides to determine all the angles and the length of the third side
True
In air navigation, bearing is an angle measured in clockwise direction from the line pointing north to the path of the plane or a line of sight
True
In marine navigation and surveying, the degree measure of a bearing can have any value between 0° and 90°
True
The equation 3cot^2 (x)+1=0 has no solutions
True
The equation sec2x - 2 = 0 has 4 solutions on the interval [0, 2π)
True
The equation sin^2(x)-sin x-12=0 has no solutions
True
The expression 2sin3xsin9x equals to
cos6x - cos12x
The expression 2cos2xcos6x equals to
cos8x + cos4x
For f(x)=x^3+1, find f^1(x)
f^-1 (x)=^3√x-1
The expression 2sin5xcos7x equals to
sin12x - sin2x
Evaluate g*f(1)
undefined
What is arcsin (π/2)?
undefined
What is g*f if f(x) = √x-1 and g(x) = x^2+2
x + 1
Find all solutions of the following equation: sin(1/3x) =-√3/2
x = -ππ + 6ππn and x = 4ππ + 6ππn, where n is an integer
Find all solutions of the equation tan^2 x-tan x-6=0 on the interval [0,2π)
x = arctan(3), x = ππ + arctan(3), x = 2ππ -arctan(2), x = ππ - arctan(2)
Solve the equation: 4sin^2 (x)-1=0
x=+π/6+πn
Find the solutions of the following equation: √2csc x +2=0
x=-π/4 + 2πn and x=5π/4 +2πn, where n is an integer
Find the solutions of the following equation: sin2x = 0
x=π/2n, where n is an integer
What is arccos(-1)?
ππ
Find the exact value of cos(arctan(-2))
√5/5