Free Printable 1-6 Solve using Pythagorean identities

1.

Simplify: $\sec^2\theta-\tan^2\theta$

a)

1

b)

-1

c)

$\csc\theta$

d)

$-\csc\theta$

2.

Which of the following is not a pythagorean identity?

a)

$\cot^2x+1=\csc^2x$

b)

$\cot^2x-\csc^2x=-1$

c)

$\csc^2x-\cot^2x=1$

d)

$\csc^2x+1=\cot^2x$

3.

Given sin⊖ = $\frac{-1}{3}$ and cos⊖ = $\frac{2\sqrt{2}}{3}$ , find the exact value for tan⊖.

a)

$-2\sqrt{2}$

b)

$\frac{\sqrt{2}}{4}$

c)

$-3$

d)

$\frac{-\sqrt{2}}{4}$

4.

Given cos ⊖ = $\frac{\sqrt{3}}{5}$ and tan⊖ < 0 , find the exact value for sin⊖ using pythagorean identities.

a)

$\frac{5\sqrt{3}}{3}$

b)

$\frac{\sqrt{22}}{5}$

c)

$\frac{22}{25}$

d)

$\frac{-\sqrt{22}}{5}$

5.

Which expression always equals 1?

a)

$\cos^2\theta-\sin^2\theta$

b)

$\cot^2\theta+\csc^2\theta$

c)

$\tan^2\theta+\sec^2\theta$

d)

$\cos^2\theta+\sin^2\theta$

6.

The expression $\sin^2x+\cos^2x-b^2$ is equal to

a)

1

b)

$b^2$

c)

$\left(1+b\right)\left(1-b\right)$

d)

$\sin x\cos x-b$

7.

If $\cos\theta=-\frac{4}{5}$ and $\theta$ lies in Quadrant II, what is the value of $\tan\theta$ ?

a)

$-\frac{3}{4}$

b)

$-\frac{4}{3}$

c)

$\frac{3}{4}$

d)

$\frac{4}{3}$

8.

If x is a positive acute angle and $\cos x=\frac{\sqrt{3}}{4}$ , what is the exact value of $\sin x$ ?

a)

$\frac{1}{2}$

b)

$\frac{4\sqrt{13}}{13}$

c)

$\frac{\sqrt{13}}{4}$

d)

$-\frac{1}{2}$

9.

Which of the following is NOT a Pythagorean identity?

a)

$\tan^2x+1=\sec^2x$

b)

$\cos2x\ =\ \cos^2x-\sin^2x$

c)

$\sin^2x\ +\ \cos^2x=1$

d)

$1+\cot^2x\ =\ \csc^2x$

10.

Pythagorean: $\sin^2x-1=?$

a)

$-\cos^2x$

b)

$\cos^2x$

c)

$\cos^2x-1$

d)

$1-\cos^2x$

11.

Using Pythagorean Identity: $\tan^2x=?$

a)

$\sec^2x-1$

b)

$\sec^2x+1$

c)

$1-\sec^2x$

12.

Using Pythagorean Identity: $\csc^2x=?$

a)

$1+\cot^2x$

b)

$1-\cot^2x$

c)

$\cot^2x-1$

13.

Given sin⊖ = 2/3 and tan⊖ <0, find the exact value for tan⊖

a)

3/2

b)

(3√5)/5

c)

(-2√5)/5

d)

-√5/2

14.

Given sin⊖ = 2/3 and tan⊖ <0, find the exact value for cos⊖

a)

3/2

b)

-√5/3

c)

√5/3

d)

-2/3

15.

Given cos ⊖ = √13/4 and tan⊖ < 0 , find the exact value for csc⊖

a)

√3/2

b)

(-4√3)/3

c)

(4√3)/3

d)

1/2

1-6 Solve using Pythagorean identities

Total questions: 15

Worksheet time: 8mins

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