Quick help with some math problems...Trig and Precalc

[dnricks]

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

1. Find ? to four significant digits for 0 ? ? < 2? where csc ? = -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!!!

 

[mmm4444bot]

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Hello dnricks:

It takes several weeks of instruction to cover all of this material. I have no idea what you've learned about trigonometry (or algebra or geometry) so far because you have neither shown any start on these exercises nor asked any questions on your own about them. In other words, I have no idea why you're stuck because you have not said anything about what you're thinking.

I'm certainly not going to type up several weeks of instruction, for you. (Perhaps, somebody else will.) What are your expectations? How would you like us to proceed?

(1) Look up the identity for cosecant, understand in which quadrants the sine ratio is negative, understand how to use the reference angle that comes out of a scientific calculator's inverse sine function, and go from there.

(2) Please check your information; none of the given choices seem to match.

(3) Understand that x is not an angle, understand the purpose of inverse trig functions, understand that 5 and 4 are two lengths of a right-triangle, and go from there.

(4) Understand the form of a Complex number a + bi where a and b are Real numbers, look up the polar form to see r cos(theta) + r sin(theta) i, as well as formulas for calculating r and theta from a and b, understand the meaning of cis() notation, and go from there.

(5) Can you not look up the formula for the area of a circle sector? Just substitute the given values, and go from there.

(6) Understand properties of logarithms, use log(b^x)=x log(b) and log(ab)=log(a)+log(b) to simplify the equation, then switch to the exponential form, and go from there.

(7) Understand the definitions of isosceles and trapezoid, draw a picture, form right-triangles, use symmetry and sine ratios, and go from there.

(8) I'm guessing that cos-1 0.70 is supposed to mean the inverse cosine of the ratio 7/10. Again, understand the meaning of inverse trig functions, double-angle formulas, the Pythagorean Theorem, and put it all together.

Most students understand these exercises only after several weeks of instruction and practice.

What have you learned so far?

At what stage are you stuck, in each of these?

Cheers,

~ Mark

 

[sportsstar469]

do you honestly expect people to answer that. i think mark was generous in his reply thoughs.