Prove the Pythagorean identity sin²(θ) + cos²(θ) = 1 and use it to find sin(θ) cos(θ) or tan(θ) given sin(θ) cos(θ) or tan(θ) and the quadrant of the angle.

Sample Practice Questions (3)

tan (θ) = \frac{15}{8}

and

π < θ < \frac{3 π}{2}

, find the value of

sin (θ)

- \frac{15}{17}

- \frac{8}{17}

\frac{15}{17}

\frac{8}{17}

The terminal side of an angle

θ

in standard position intersects the unit circle at point

P

as shown in the diagram. If the

x

-coordinate of point

P

0.6

, what is the

y

-coordinate of point

P

0.4

- 0.4

0.8

- 0.8

Look at the unit circle diagram below. If the angle

θ

21 0^{\circ}

, which statement correctly uses the Pythagorean identity to verify the coordinates of the point on the circle?

(- \frac{3}{2})^{2} + (- \frac{1}{2})^{2} = 1

(\frac{3}{2})^{2} + (\frac{1}{2})^{2} = 1

(- \frac{1}{2})^{2} + (- \frac{3}{2})^{2} = 0.5

(- \frac{2}{2})^{2} + (- \frac{2}{2})^{2} = 1

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