Question

Find the values of the trigonometric functions of t from the given information.

sec(t) = 6, sin(t) < 0
need sin(t, cos(t), csc(t), tan(t), cot(t)

Answer 1

To find the values of the trigonometric functions of t, we can use the relationships between the trigonometric functions. Given that sec(t) = 6 and sin(t) < 0, we can find the values of sin(t), cos(t), csc(t), tan(t), and cot(t).

Step-by-step explanation:

To find the values of the trigonometric functions of t, we are given that sec(t) = 6 and sin(t) < 0. We can use the relationship between the trigonometric functions to find the values of sin(t), cos(t), csc(t), tan(t), and cot(t).

From sec(t) = 6, we know that cos(t) = 1/sec(t) = 1/6. Since sin(t) < 0, we can determine that sin(t) = -sqrt(1 - cos^2(t)) = -sqrt(1 - (1/6)^2) = -sqrt(35)/6.

From sin(t) and cos(t), we can find the values of csc(t), tan(t), and cot(t) using the reciprocal relationships. csc(t) = 1/sin(t), tan(t) = sin(t)/cos(t), and cot(t) = 1/tan(t).

Therefore, sin(t) = -sqrt(35)/6, cos(t) = 1/6, csc(t) = -6/sqrt(35), tan(t) = -sqrt(35), and cot(t) = -1/sqrt(35).

Answer 2

sec (t) is the inverse function of cos (t) that is the function becomes cos (t) = 1/6. if sin (t) < 0 then t is in the  fourth quadrant. This means t is equal to 279.59 degreees. sin t is equal to -0.986, cos t is equal to 1/6, tan t is equal to -5.92 and cot (t) is equal to -0.169