Question

If sin(t)=15/17 and tan(t)=15/8, what is sec(t)?

A) 17/5
B) 8/15
C) 17/8
D) 1/cos(t)

Answer 1

To find sec(t) given sin(t) = 15/17 and tan(t) = 15/8, calculate the reciprocal of cos(t), which is gained from dividing sin(t) by tan(t). The result is sec(t) = 17/8.

Step-by-step explanation:

If sin(t) = 15/17 and tan(t) = 15/8, to find sec(t), which is equivalent to 1/cos(t), we would use trigonometric identities and relationships between these functions. First, recall that tan(t) = sin(t)/cos(t). If we solve for cos(t) using the given value for tan(t), we can say cos(t) = sin(t)/tan(t), which will give us cos(t) when we plug in the known values. So, cos(t) = (15/17) / (15/8) = 8/17.

Now that we have cos(t), to find sec(t), we simply take the reciprocal of cos(t) which results in sec(t) = 1/(8/17) = 17/8. Hence, the correct answer is (C) 17/8.