Suppose that cos(t) = 8/17 and t is in the 4th quadrant. evaluate sin(t+t) to 2 decimal places.

sin(t+t) = 0.83

Step-by-step explanation:

cos (t) = 8/17 we know that cos x = adjacent side / hypotenuse

(You can take a look at the image below to give you an idea of how it looks)

The problem asks us to evaluate sin (t + t) = sin (2t), however we have a formula to help us find this in terms of t:

sin (2t) = 2(sint)(cost)

So now we need to find sin(t)

OS² = 17² - 8² = 289 - 64 = 225

OS = √225

OS = 15

But since the angle is in the 4th quadrant, then the OS = -15.

Therefore, sin(t) = opposite side / hypotenuse = -15/17

Now we have sin (t) = -15/17 and cos(t) = 8/17 and we can substitute this in the formula for sin (2t)

Therefore, sin(2t) = 0.83 (rounded to two decimal places)