Trig Funct of Gen Angles

# Given that the point 5 12 is on the terminal side of

This preview shows pages 8–13. Sign up to view the full content.

Given that the point (5, -12) is on the terminal side of an angle θ , find the exact value of each of the 6 trig functions. (5, -12) 5 -12 13 = = = = = = θ θ θ θ θ θ cot tan sec cos csc sin θ α We'll call the reference angle α . The trig functions of θ are the same as α except they possibly have a negative sign. Labeling the sides of triangles with negatives takes care of this problem. 12 13 o h - = 13 5 = h a 12 5 o a - = 12 13 - = o h 5 13 = a h 12 5 - = o a

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
In quadrant I both the x and y values are positive so all trig functions will be positive + + α All trig functions positive In quadrant II x is negative and y is positive. _ + α We can see from this that any value that requires the adjacent side will then have a negative sign on it. Let's look at the signs of sine, cosine and tangent in the other quadrants. Reciprocal functions will have the same sign as the original since "flipping" a fraction over doesn't change its sign. sin is + cos is - tan is -
_ _ α In quadrant IV, x is positive and y is negative . _ + α So any functions using opposite will be negative. Hypotenuse is always positive so if we have either adjacent or opposite with hypotenuse we'll get a negative. If we have both opposite and adjacent the negatives will cancel sin is - cos is + tan is - In quadrant III, x is negative and y is negative. sin is - cos is - tan is +

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
All trig functions positive sin is + cos is - tan is - sin is - cos is + tan is - sin is - cos is - tan is + To help remember these sign we look at what trig functions are positive in each quadrant. A S T C Here is a mnemonic to help you remember. (start in Quad I and go counterclockwise) All Students Take Calculus
What about quadrantal angles? We can take a point on the terminal side of quadrantal angles and use the x and y values as adjacent and opposite respectively. We use the x or y value that is not zero as the hypotenuse as well.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern