# Given #csctheta^circ=sqrt3/2# and #sectheta^circ=sqrt3/3#, how do you find #sintheta#?

There is no solution to this question.

By signing up, you agree to our Terms of Service and Privacy Policy

Given ( \csc(\theta) = \frac{\sqrt{3}}{2} ) and ( \sec(\theta) = \frac{\sqrt{3}}{3} ), you can find ( \sin(\theta) ) using the following steps:

- Recall that ( \csc(\theta) ) is the reciprocal of ( \sin(\theta) ), and ( \sec(\theta) ) is the reciprocal of ( \cos(\theta) ).
- Use the given values to find ( \sin(\theta) ) and ( \cos(\theta) ) reciprocals.
- Apply the Pythagorean identity ( \sin^2(\theta) + \cos^2(\theta) = 1 ) to find ( \sin(\theta) ).
- Once you have ( \sin(\theta) ), verify its sign using the given values to ensure it is correct.

Calculating ( \sin(\theta) ) using the reciprocals of ( \csc(\theta) ) and ( \sec(\theta) ), you would have:

[ \sin(\theta) = \frac{1}{\csc(\theta)} = \frac{1}{\frac{\sqrt{3}}{2}} = \frac{2}{\sqrt{3}} ]

Then, rationalize the denominator:

[ \sin(\theta) = \frac{2}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{2\sqrt{3}}{3} ]

Thus, ( \sin(\theta) = \frac{2\sqrt{3}}{3} ).

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- The hypotenuse of a 30°- 60°- 90° right triangle measures 22 cm. What are the lengths of the longer leg and shorter leg?
- Find the general value of (theta) satisfying: 1) sin2(theta)=1/2 2) cos2(theta)=1/2 3) tan3(theta)=1/√3 4) cos3(theta)=-√3/2 5) sin²(theta)=3/4 6) sin²2(theta)=1/4 7) 4cos²(theta)=1 8) cos²2(theta)=3/4??
- How to write 2sinθ - 4cosθ in the form rsin(θ - α)?
- How do you evaluate #Cos((2pi)/9)#?
- If #tan x=6/8#, how do you find cos x?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7