1. Help with a few problems please..

If anyone could help me with a few trig problems, that would be amazing!!!

1. Find θ to four significant digits for 0 ≤ θ < 2π where csc θ = -1.401
A. 0.6199, 8.805
B. 0.7949, 5.488
C. -2.776, 3.936
D. 3.936, 5.488

2. Simplify the expression: cos(x – y)cos y - sin(x + y)sin y
A. cos x
B. cos (x-2y)
C. sin x
D. cos (x+2y)

3. Find the exact value of x. cos^-1 (x) = csc^-1 (5/4)
A. (√41)/4
B. 3/4
C. 3/5
D. (√41)/5

4. Write the complex number in polar form. -4√2 + 4i√2
A. 8 cis (-135°)
B. 8 cis 45°
C. 8 cis 135°
D. 8 cis (-45°)

5. Find the central angle, x, of a circle of radius 264.2 m and the area of the sector is 69.8 m2.
A. 0.00314
B. 0.00100
C. 0.00400
D. 0.00200

6. Solve the equation, 4 log 4 + log x = 6
A. 3906.2500
B. 2.56 * 108
C. 62,500.0000
D. 8994.4730

7. A patio is designed in the shape of an isosceles trapezoid with bases 5.0 m and 7.0 m. The other sides are 6.0 m each. Write one or two paragraphs explaining how to use the sine to find the internal angles of the patio.

8. In checking the angles of a section of a bridge support, an engineer finds the expression sin(2 cos-1 0.70). Write a paragraph explaining how the value of this expression can be found without the use of a calculator.

Thanks so much if you can help me out!!!

2. Hello dnricks

Welcome to Math Help Forum!
Originally Posted by dnricks
If anyone could help me with a few trig problems, that would be amazing!!!

1. Find θ to four significant digits for 0 ≤ θ < 2π where csc θ = -1.401
A. 0.6199, 8.805
B. 0.7949, 5.488
C. -2.776, 3.936
D. 3.936, 5.488

2. Simplify the expression: cos(x – y)cos y - sin(x + y)sin y
A. cos x
B. cos (x-2y)
C. sin x
D. cos (x+2y)

3. Find the exact value of x. cos^-1 (x) = csc^-1 (5/4)
A. (√41)/4
B. 3/4
C. 3/5
D. (√41)/5

4. Write the complex number in polar form. -4√2 + 4i√2
A. 8 cis (-135°)
B. 8 cis 45°
C. 8 cis 135°
D. 8 cis (-45°)

5. Find the central angle, x, of a circle of radius 264.2 m and the area of the sector is 69.8 m2.
A. 0.00314
B. 0.00100
C. 0.00400
D. 0.00200

6. Solve the equation, 4 log 4 + log x = 6
A. 3906.2500
B. 2.56 * 108
C. 62,500.0000
D. 8994.4730

7. A patio is designed in the shape of an isosceles trapezoid with bases 5.0 m and 7.0 m. The other sides are 6.0 m each. Write one or two paragraphs explaining how to use the sine to find the internal angles of the patio.

8. In checking the angles of a section of a bridge support, an engineer finds the expression sin(2 cos-1 0.70). Write a paragraph explaining how the value of this expression can be found without the use of a calculator.

Thanks so much if you can help me out!!!
Let me suggest one or two things first:

• Post only one question at a time. (Have a look at the Rules - particularly #14.)

• If you can show us the attempt that you've made, that will help to identify exactly where the problem is. As it is, it just looks as if you want someone to do your homework for you!

Having said that, let me give you some clues for the first two questions:

(1) I'm sure you know that $\csc x=\frac{1}{\sin x}$. So use a calculator to find the principal value. Then look at how the values of $\sin x$ (and therefore $\csc x$ repeat: $\sin x = \sin(\pi-x) = \sin(2\pi + x) = \sin(3\pi - x) = ...$

(2) Do you know the formulae:

• $\cos(A+B)+\cos(A-B)=2\cos A \cos B$
• $\cos(A-B)-\cos(A+B)= 2 \sin A\sin B$
• $\cos A + \cos B = 2\cos\tfrac12(A+B)\cos\tfrac12(A-B)$?

Use them!