Quick easy cosine question?

Question

Hey everyone, I'm having trouble with a seemingly simple problem.

70 cos A = -7
cos A = -0.1

How do I find A now? >.>

The book says the answer is 95.739 Degrees but I'm confused on how I get that number from cos A = -0.1

Thanks for any help you can provide!

Got it, knew that button was used for something =P

Thanks guys!

Answer 1

make sure your calculator is in degree mode if your using one. Next you need to take the inverse cosine of -0.1. Its the button with cosine to the negative one power. Your answer should be 95.739 degrees.

Answer 2

The sine function is the ratio of the y axis dimension to the hypotenuse on the Cartesian coordinate system. The hypotenuse is always positive. Thus sine is positive wherever the y axis is positive and negative elsewhere. So sine is positive in quadrants 1 and 2 and negative in quadrants 3 and 4. Similarly, cosine is the ratio of the x axis dimension to the hypotenuse. So cosine is positive in quadrants 1 and 4 and negative in quadrants 2 and 3. Therefore cos A = -0.1 must be in either quadrant 2 or 3. Apparently, in your problem they are restricting the domain to values between zero and 180 degrees which makes the quadrant 2 value the correct answer. As soon as you have a negative value for cosine, it is known the angle must be between 90 and 180 degrees. The reference angle is 84.261 degrees which gives cos = 0.1 and subtracting this from 180 degrees gives 95.739 degrees.

Answer 3

By using the inverse function, a=arccos(-0.1).
Or, if you are using tables, look what angle corresponds to cos(0.1) and subtract it from 180° to account for the negative sign.

Answer 4

cos A = - 0.1
Due to - ve sign, A is in 2nd and 3rd quadrants.
arc cos 0.1 = 84.3°
Thus A = 180° - 84.3° = 95.7°
and A = 180° + 84.3° = 264.3°

Answer 5

Use the inverse cosine function on your calculator.
Cos^-1