Linking Geometry and Trig

[brit2011]

My teacher gave us a worksheet to link geometry to trigonometry. It is in the following attachment because I thought it would be helpful to see the circles. I was able to figure out the first problem, but after that I am at a complete loss as to what to do. Any help?

 

[fasteddie65]

My teacher gave us a worksheet to link geometry to trigonometry. It is in the following attachment because I thought it would be helpful to see the circles. I was able to figure out the first problem, but after that I am at a complete loss as to what to do. Any help?

?OAK ~ ?OTA because of AA Similarity Theorem. Both triangles have angle theta (I'll use ø for theta), and both triangles have a right angle.

Then, because corresponding sides of similar triangles are proportional, AB/TA = OB/OA. So TA = AB • OA/OB = 1 • sin ø/cos ø = tan ø.

By using other proportions with similar triangles, you can get the other trigonometric values.

 

[brit2011]

ohhhh. okay that makes sense. thank you so much!

 

[brit2011]

so would this be right to prove that TO is sec theta (idk how to write theta):
TO/OA=OA/OB. TO=OA x OA/OB. TO= 1 x 1/costheta. since 1/costheta is sec TO is sectheta.

 

[fasteddie65]

That's the idea.

 

[brit2011]

alright thanks! i have one more question. it asks us to find the measure of angle COA. i know that angle COT is a right angle so in theory you would just subtract theta from 90, but how do i know what theta is?