Question

Find the exact value of the trigonometric expression given that sin(u) = − 3 5 , where 3π/2 < u < 2π, and cos(v) = 15 17 , where 0 < v < π/2. tan(u + v)

Answer 1

Answer:

-13/84

Step-by-step explanation:

Calculation to Find the exact value of the trigonometric expression

First step is to find tan(u)

Based on the information given we were told that sin(u) = -3/5 which means if will have -3/5 in the 4th quadrant would have triangle 3-4-5

Hence:

tan(u)=-3/4

Second step is to calculate tan(v)

In a situation where cos(v) is 15/17 which means that we would have triangle 8-15-17

Hence:

tan(v) = 8/15

Now Find the exact value of the trigonometric expression using this formula

tan(u+v) = (tan(u) + tan(v))/(1-tan(u)tan(v)

Where,

tan(u)=-3/4

tan(v)=8/15

Let plug in the formula

tan(u+v)=(-3/4)+(8/15)÷[1-(-3/4)(8/15]

tan(u+v)=(-45+32)÷(60-24)

tan(u+v)=-13/84

Therefore exact value of the trigonometric expression will be -13/84