Question

If ( sin y^circ = s/8) and ( tan y^circ = s/t) , what is the value of ( cos y^circ )?

a) √'(64 - s^2)/8)
b) √'(64 - s^2)/t
c) 8/√(64 - s^2
d) t/√'(64 - s^2

Answer 1

The value of cos y° is √(64 - s²)/8, obtained by rearranging the Pythagorean identity and substituting the given value of sin y°.

Step-by-step explanation:

To find the value of cos y°, we can use the Pythagorean identity which states that:

sin² y + cos² y = 1

We are given sin y° = s/8, so to find cos y° we rearrange the Pythagorean identity to:

cos² y = 1 - sin² y

Substituting sin y°, we get:

cos² y = 1 - (s/8)²

Thus, cos y° = √(1 - (s/8)²). Because cos y° must be positive (as it is not provided whether y falls in a quadrant where cosine is negative), we have:

cos y° = √(64 - s²)/8

Therefore, the correct option is a) √(64 - s²)/8.