Use the trig Identities to find the other 5 trig functions.

Problem
7.)Tan(90-x)=-3/8
8.)Csc x=-13/5
9.)Cot x=square root of 3
10.)Sin(90-x)=-.4563
11.)Sec(-x)=4
12.)Cos x=-.2351
I need HELP!

I will do one for you.

You try some of the others and let me know what you got.

#8
csc x = -13/5, then
sin x = -5/13

so by CAST, angle x is in either III or IV

construct a right-angled triangle with the side opposite angle x as 5 and hypotenuse 13 (sin ß = opp/hyp)
By Pythagoras the adjacent side is 12

so in III, (x is appr. 202.62º)
sin x = -5/13
cos x = -12/13
sec x = -13/12
tan x = 5/12
cot x = 12/5

in IV, (x is appr. 337.38º)
sin x = -5/13
cos x = 12/13
sec x = 13/12
tan x = -5/12
cot x = -12/5

Would #7 be Sin- 3 over square root of 73 Cos- 8 over square root of 73 Tan- -8/3 Csc- square root of 73 over 3 Cot- -3/8

sin x =4/5 and cos y = 5/3

sin x = 4/5
cos x = 3/5
soc^2 x = 5/3- answer

Sure, I can help you with that! To find the other trigonometric functions, we can use the definitions and identities of the trigonometric functions. Let's go through each of the given problems one by one.

7.) Tan(90-x) = -3/8

Since Tan is the ratio of sine to cosine, we can write this equation as follows:
Sin(90-x)/Cos(90-x) = -3/8

Using the trigonometric identity for complementary angles, we know that Sin(90-x) = Cos(x). Similarly, Cos(90-x) = Sin(x).
Therefore, the equation turns into:
Cos(x)/Sin(x) = -3/8

To solve for x, we can cross-multiply:
8 * Cos(x) = -3 * Sin(x)

Now, we can use the Pythagorean identity Sin^2(x) + Cos^2(x) = 1 to rewrite the equation:
8 * Cos(x) = -3 * (1 - Cos^2(x))
8 * Cos(x) = -3 + 3 * Cos^2(x)

Rearranging the equation:
3 * Cos^2(x) + 8 * Cos(x) - 3 = 0

Now, solve this quadratic equation for Cos(x) using factoring, quadratic formula, or any other method.

8.) Csc x = -13/5

Csc is the reciprocal of Sin. So, we can write this equation as:
1/Sin(x) = -13/5

Cross-multiplying, we have:
5 = -13 * Sin(x)

Dividing both sides by -13, we get:
Sin(x) = -5/13

Now, you can either use a calculator or reference values from the unit circle to find the sine inverse of -5/13.

9.) Cot x = sqrt(3)

Cot is the reciprocal of Tan. We can write this equation as:
1/Tan(x) = sqrt(3)

Replacing Tan with Sin/Cos, we get:
Cos(x)/Sin(x) = sqrt(3)

Cross-multiplying:
Cos(x) = sqrt(3) * Sin(x)

Using the Pythagorean identity Sin^2(x) + Cos^2(x) = 1, we substitute in the equation:
1 - Sin^2(x) = 3 * Sin^2(x)

Rearranging, we get:
4 * Sin^2(x) = 1

Taking the square root of both sides:
2 * Sin(x) = ±1

Solving for Sin(x), we have:
Sin(x) = ±1/2

Now, you can find the sine inverse of ±1/2.

10.) Sin(90-x) = -0.4563

Using the trigonometric identity for complementary angles, we know that Sin(90-x) = Cos(x).
So, the equation turns into:
Cos(x) = -0.4563

11.) Sec(-x) = 4

Sec is the reciprocal of Cos. We can write this equation as:
1/Cos(-x) = 4

Cos(-x) is equal to Cos(x) because cosine is an even function.
So, the equation becomes:
1/Cos(x) = 4

12.) Cos x = -0.2351

These are straightforward equations that you can solve directly to find the value of x. Use a calculator if needed.

I hope this helps you solve the problems! Let me know if you have any further questions.