Honors Precalculus Unit 1-Trig

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Simplify cot^2 x - csc^2 x

-1

Evaluate. Tan (arctan -5)

-5

Simplify. tan x - (sec^2 x)/tanx

-cot x

Evaluate. arcsin (-1/2)

-pi/3

Prove -(cot x)/csc x = -cos x

Prove the identity.

Prove the following identity: (tanx)/(1-sec x) + (1+sec x)/tan x

Prove the identity.

Solve. cos (x/2)=sqrt (2)/2

x = pi/2 + 4n pi x=7pi/2 + 4npi

Solve3 cot^2x - 1 = 0

x = pi/3 + n pi x=2pi/3 + npi

Evaluate arcsin(sin 3 pi)

0

Evaluate sin(arcsin (0.1))

0.1

Simplify: (cos^2 x - 4)/(cos x - 2)

cos x + 2

Evaluate arcsin 2

undefined

Solve 2sin^2 (2x) = 1

x = pi/8 +npi/4

Solve. 3 csc^2 x -4 = 0

x=pi/6 + npi x=5pi/6 + npi

Evaluate: sin(arctan 4/3)

4/5

Evaluate. cot(arctan(5/8)

8/5

Prove: cot^2 y (sec^2 y - 1) = 1

Prove the identity.

Evaluate arctan (-1)

pi/4

Evaluate arctan -1

-pi/4

Evaluate. arctan (-1)

-pi/4

Evaluate. arctan(-(sqrt 3)/3

-pi/6

Simplify: sin x cos^2 x - sin x

-sin^3 x

Simplify: (csc x - cot x)(css x + cot x)

1

Simplify: (sec x)(sin x/tan x)

1

Evaluate arccos (-(sqrt 2)/2)

3pi/4

Evaluate. arccos (-sqrt 2/2)

3pi/4

Evaluate sin(arctan 4/3)

4/5

Evaluate. cos(arcsin -3/5)

4/5

Evaluate arccos (-(sqrt 3)/2)

5pi/6

Evaluate. arcsin sqrt 3/2

60 degrees

Evaluate cos(arccos pi)

No solution

Prove cos 9-x)/(1-sin (-x))=sec x + tan x

Prove the identity

Prove: (1 + cos x)/sinx + sinx/(1+cos x) = 2 csc x

Prove the identity

Prove: (tan^3 x - 1)/(tanx - 1) = tan^2 x + tan x + 1

Prove the identity

Prove: sin ^(1/2) x cos x - sin ^(5/2) x cos x=cos^3 x sqrt sin x

Prove the identity

Prove the identity. cos x/(1-sin x) = sec x + tan x

Prove the identity.

Prove: (sec x - tan x)(csc x + 1) = cot x

Prove the identity.

Prove: tan x + cot x = sec x csc x

Prove the identity.

Know your fundamental identities. They will not be provided for you on any quiz or test.

This includes the reciprocal, cofunction, pythagorean, even/odd, and quotient identities.

Simplify 1/(tan^2 x)

cos^2 x

Prove the following identity: cos^2 x + cos ^2 (pi/2 -x) = 1

cos^2 x + sin^2 x = 1

Simplify. 1 - 2 sin^2 x + sin^4 x

cos^4 x

Evaluate. arcsin 1

pi/2

arctan(tan 7pi/3)

pi/3

Evaluate arcsin (sqrt 2/2)

pi/4

Evaluate arctan sqrt3/3

pi/6

Evaluate.arcsin(sin 13pi/6)

pi/6

Evaluate. tan(arccos 2/3)

sqrt 5/2

sin(arccos (-2/3))

sqrt(5)/3

Simplify: sinx sec x

tan x

Simplify sin^2 x/(1 - sin^2 x)

tan^2 x

Simplify. tanx sec x + sec^2 x

tan^2 x + tan x + 1

Solve: sqrt 3 sec x - 2 = 0

x = 5pi/6 + 2npi x = 7pi/6 + 2npi

Solve: tan 3x (tan x - 1) = 0

x = npi/3 x= pi/4 + npi

Solve. (3tan^2 - 1)(tan^2 x - 3) = 0

x = pi/6 + npi x=5pi/6 + npi x = pi/3 + npi x=2pi/3 + npi

Solve: 2 sin^2 (2x) = 1

x = pi/8 + npi/4

Solve. tan^2 (3x) = 3

x = pi/9 + npi/3 x = 2pi/9 + npi/3


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