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