Pre Cal Unit 6
Simplify: sec^2θcos^2θ
(1/ cos^2θ) cos^2θ = 1 or secθ (1/secθ) = 1 1
Given the value of the function, find the value of the indicated function. Use a calculator if needed. sinθ= 4/5 in quadrant II Find cosθ
-3/5
Given the value of the function, find the value of the indicated function. Use a calculator if needed. 4 tan θ = 3 in quadrant III Find csc θ, Use cot θ = 3/4
-5/4
Solve using the power reducing identities. Find cos^2u ; u = 70°
0.1170
Write the reciprocal: tanθ
1 cotθ
Given the value of the function, find the value of the indicated function. Use a calculator if needed. tanθ = 4/3 in quadrant III
3/4
trigonometry examines trigonometric identities and the connection between trigonometric functions.
Analytical
The identity, sin^2θ + cos^2θ = 1 is a __________________ identity.
Pythagorean
Variation
a different form.
. Simplify the expression. Use a sum-and-difference formula and a calculator. cos(u+2π)
cos u
Fill in the blank: sin^2θ+_____= 1
cos^2θ
Simplify: cot^2θ−cot^2θcos^2θ
cot^2θ (1-cos^2θ), cot^2θ sin^2θ, cos^2θ (sin^2θ) = cos^2θ sin^2θ cos^2θ
Arbitrarily
determined by chance, whim, or impulse.
Analytical
proving by reasoning.
Simplify the expression. Use a sum-and-difference formula and a calculator. tan(u+π)
tan u
Simplify the expression. Use a sum-and-difference formula and a calculator. tan(u- π/4)
tan u - 1 tan u + 1
Use the identities to rewrite the expression as a single trigonometric function: sin(π/3) cos(π/3)
tan(π/3)
Fill in the blank: ________ +1=sec^2θ
tan^2θ
Simplify: cot^2θ − csc^2θ
-1
Simplify: tanθcosθ
sinθ
Solve using the power reducing identities and a calculator. Find sin^2u ; u = 0.5236 rad
0.2500
Solve using the power reducing identities and a calculator. Find cos^2u ; u=45°
0.5000
derive
get, receive.
Integral
measure of the area under a graph of a function.
Fill in the blank: csc^2θ=cot^2θ+_____
1
Simplify the expression. Use a sum-and-difference formula and a calculator. cos (u−2π)
cos u
Use the identities to rewrite the expression as a single trigonometric function: cos 10° sin 10°
cot 10°
Solve. Use a calculator if needed. cos50∘ sin50∘
cot50∘
Given the value of the function, find the value of the indicated function. Use a calculator if needed. tanθ = 2 in quadrant III (round the answer to two decimal places) cscθ Use cotθ = 0.50 to get this answer
cot^2θ+1 = csc^2θ, (1/2)^2 +1 =csc^2θ, csc^2θ =1/4 +1= 4/5, cscθ= √5/4 = √5/4 = √5/2= −1.12 1.12
Analytical is proving by
reasoning
Pythagorean
referring to Pythagoras, who described reality in terms of arithmetic relationships.
Prove the identity algebraically. secθ = 1/cosθ
secθ =hyp/adj cosθ = adj/hyp 1/cosθ = 1 ⋅adj/hyp 1/cosθ = 1×hyp/adj=hyp/adj Therefore secθ =1 cosθ
Use the identities to rewrite the expression as a single trigonometric function: 1 csc 52∘
sin 52∘
Simplify the expression. Use a sum-and-difference formula and a calculator. cos (u- π/2)
sin u
Simplify the expression. Use a sum-and-difference formula and a calculator. tan (u−5π)
tan u
Simplify: sin^2θ + cos^2θ + tan^2θ − 1
tan^2θ
Simplify the expression. Use a sum-and-difference formula and a calculator. cos(u+π)
−cos u
Solve. Do not use the calculator. Find cos 15∘ using 45∘ and 30∘
√+ 6 + √+2 4
Use a calculator and find to 4 decimal places the value of the trigonometric function using the given identity. 2u=64°, cos2u = 1 − 2 sin^2u
0.4384
Use a calculator and find to 4 decimal places the value of the trigonometric function using the given identity. u=48°, tan (1/2)u = 1-cosu/sinu
0.4452
Use a calculator and find to 4 decimal places the value of the trigonometric function using the given identity. u=110°u=110° , cos(1/2)u = ± 1+cosu/2
0.5736
Solve. Use the calculator set for degrees. Round answers to 4 decimal places. Find sin 45° using 15° and 30°
0.7071
Solve. Use the calculator set for degrees. Round answers to 4 decimal places. Find sin 45° using 60° and 15°
0.7071
Use a calculator and find to 4 decimal places the value of the trigonometric function using the given identity. 2u = 14°, cos^2u = cos^2u − sin^2u
0.9703
Use a calculator and find to 4 decimal places the value of the trigonometric function using the given identity. 2u = 82°, sin^2u = 2sinu cosu
0.9903
Prove the power reducing identity: cos^2 u = 1+cos^2u/2
1+ cos2u = 2cos^2 u, 2cos^2u = 1 +cos2u, cos^2u = 1+cos2u/ 2
Use the sum and difference formulas with sin^2 u + cos^2 u = 1 to find the value. sin u = 3/5 and cos u = 12/37 in quadrant I Find sin(u+v)
176/185
Use the sum and difference formulas with sin^2u + cos^2u =1 to find the value. sinu = 1/2 and cos v 2/3 in quadrant II Find cos(u+v)
2√3 − √5 6
Identity
an expression that is true for any number that replaces the variable.
Simplify the expression. Use a sum-and-difference formula and a calculator. sin (u+π/2)
cos u
Given the value of the function, find the value of the indicated function. Use a calculator if needed. tanθ = 2 in quadrant III round the answer to two decimal places)
cotΘ= 1 = 1 = 0.50 tanθ 2 0.50
Prove the identity algebraically. cotθ= cotθ sinθ
cotθ= cosθ sinθ adj cotθ= hyp opp hyp cotθ= adj divided by opp hyp hyp cotθ= adj X hyp = adj hyp opp opp
Use the identities to rewrite the expression as a single trigonometric function: 1 sin36°
csc36°
Complete the blank: tanθ
sinθ cosθ
Given the value of the function, find the value of the indicated function. Use a calculator if needed. tanθ = 2 in quadrant III (round the answer to two decimal places) secθ
tan^2θ+1 = sec^2θ, 2^2+1 = sec^2θ, 4+1= sec^2θ, sec^2θ = 5, secθ = √5= −2.24 -2.24
Prove the identity algebraically. tanθ = 1/ cot θ
tanθ=opp/adj 1/cotθ = 1/adj/opp 1/cotθ = 1 ⋅adj/opp 1/cosθ = 1×opp/adj = opp/adj therefore, tanθ = 1cotθ