Answer:
3. sinx = 15/17, cosx = 8/17, tanx = 15/8
4. sinx = -6/√61, cosx = 5/√61, tanx = -6/5
5. sinx = 0, cos x = -1, tanx = 0
Step-by-step explanation:
It's important to know two basic trigonometric relations:
- sin^2 x + cos^2 x = 1
- tan x = sin x / cos x
Now let's start.
3. We are given cos x = 8/17. That means that:
sin^2 x + (8/17)^2 = 1
sin^2 x + 64/289 = 1
sin^2 x = 225/289
sin x = 15/17 or -15/17
It is also given that the angle is between 0 and 90° which means that it's in the first quadrant of the unit circle. In the first quadrant, both sin and cos are positive, which means that sin x = 15/17
Finally:
tan x = 15/17 / 8/17
tan x = 15/8
4. Using the same basic trigonometric relations, we can again solve the problem. If:
sin^2 x + cos^2 x = 1
then:
sin x = √(1 - cos^2 x), √ is square root
Since we are given tan x = -6/5 we can plug it all in:
-6/5 = √(1 - cos^2 x) / cos x
now we square this to get:
36/25 = 1 - cos^2 x / cos^ x
36cos^2 x = 25 - 25cos^2 x
cos^2 x = 25/61
cos x = 5/√61 or -5/√61
We are also given that sin x is negative and since tan x is also negative, cos x has to be positive, so cos x = 5/√61
sin^2 x + 25/61 = 1
sin^2 x = 36/61
sin x = 6/√61 or -6√61
Since sin x is negative, that means sin x = -6/√61
5. Sinus if an angle is 0 if the angle is 0 (360°) or 180°. These are special angles that are usually required to be memorized. For the angle 0 (360°) sin is 0 and cos is 1 where as for angle 180° sin is 0 and cos is -1.
We are given that cos in negative, which means cos x is -1.
Now it's easy to find tan x = 0 / -1 which is 0.
