Trigonometry help?

Question

The examples don't explain how to solve these.

"find two solutions of the equation. give your answers in both degrees and radians. do not use a calculator".

a.) Sin : 1/2


b.) cot: -1



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Use a calculator to approximate two values of the angle (has to be less than 360 degrees) that satisfy the equation.


1. sin = 0.8191
2. csc= -1.0038
3. sec= -1.2241

Is there a set of rules on how to do these? Please try to explain step by step.


Thank you so much in advance.

When they say sin=1/2, they mean it as a whole, right?

y=1/2

or y/r is 1/2?

Answer 1

Oh I just did this, actually. For A and B, you have to use this: http://library.thinkquest.org/20991/media/alg2_radians.gif Remember, sin is y and cos is x.

Therefore, for letter A, look at all of the y's that are 1/2. In radians, the answer is pie/6, 11pie/6, 7pie/6, and 5pie/6. The degrees are 30, 150, 210, and 300.

P.S. It means that 1/2 is just y (not y/r).

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For numbers 1, 2, and 3, type in the inverse on a calculator. For number one, type in the inverse sin of .8191, which is 56 degrees. Then you need to figure out what quadrants it is in. All positive numbers are placed in the 1st quadrant, and postive sins are placed in the 2nd quadrant.

It's a very hard to explain it on here. The first quadrant is the same as the angle you get. The 2nd quadrant is 180 - the angle (and you do this if you have a positive sin). The 3rd quadrant is 180 + the angle (you do this with a positive tan). The 4th is 360 - angle (do this with a positive cos).

Therefore, the two answers for number one are 56 and 124 (180 - 56).

Answer 2

Learn your unit circle silly!

a) ask yourself where is sin positive? quadrant 1 and 2
sin= 1/2 -- on your unit circle it equals to 30 degrees
So your answers are 30 and (180-30) = 150

b)cot = cos/sin (memorize those ratios!!!)
ok so where is cot/tan negative? quadrant 2 and 4
and where do sin and cos equal each other on the unit circle so when they're divided they equal one? 45 degrees!!
Quad 2 = 180 - 45 = 135
Quad 4 = 360 - 45 = 315

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In these you have to do inverse of the trig ratios
1. sin^-1 (0.8191)
You'll get an angle in quadrant 1 and then you find the other in quad 2 since sin is positive in quad 1 and 2

2. where is sin negative? quad 3 and quad 4
you'll get an angle in quad 1, then from that angle to find
quad 3 angle you go 180 + angle given
quad 4 angle you go 360 - angle given

3. sec is negative (same as cos) in 2 and 3
angle given will be in quad 1, to find
quad 2 angle go 180 - angle given
quad 3 angle go 180 + angle given

You really really really need to learn the CAST rules and the unit circle. If not, trig will be BRUTAL

Answer 3

Did you know that Pythagoras was a vegetarian. Fascinating, huh? That's the limit of my knowledge on trigonometry though.