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Back to Exercise: Pythagorean identity and basic trig identities

Pythagorean Identity and Basic Trig Identities

Grade 10·25 problems·~37 min·ACT Math·topic·act-geo-trig-pythagid
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A

Recall / Warm-Up

1

In a right triangle, which ratio defines sin⁡θ\sin\theta?

Unit circle with point P at angle θ in Quadrant I, labeled (x, y), with dashed projections to the x-axis and y-axis.
2

A point on the unit circle at angle θ\theta has coordinates (x,y)(x, y). Which statement is correct?

Unit circle with x and y axes and the four quadrants labeled with Roman numerals I through IV.
3

In which quadrants is cosine negative?

B

Fluency Practice

1

If sin⁡θ=35\sin\theta = \frac{3}{5} and θ\theta is in Quadrant I, what is cos⁡θ\cos\theta? Express your answer as a fraction.

2

If cos⁡θ=513\cos\theta = \frac{5}{13} and θ\theta is in Quadrant I, what is sin⁡θ\sin\theta? Express your answer as a fraction.

3

If tan⁡θ=2\tan\theta = 2 and θ\theta is in Quadrant I, what is sec⁡θ\sec\theta? Express your answer in simplified radical form.

4

If sin⁡θ=513\sin\theta = \frac{5}{13} and θ\theta is in Quadrant II, what is tan⁡θ\tan\theta?

5

If tan⁡θ=2\tan\theta = 2 and θ\theta is in Quadrant I, what is sin⁡θ\sin\theta? Express your answer in simplified radical form with a rationalized denominator.

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