Trig Functions of Any Angle: Evaluating Trigonometric Functions Using Coordinates
Learn how to evaluate trigonometric functions of angles using coordinates on the terminal side, even if the point is not on the unit circle. Understand the relationships between sine, cosine, secant, cosecant, tangent, and cotangent functions. Practice finding trigonometric values for different points and quadrants.
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Presentation Transcript
Chapter 14 Day 5 Trig Functions of Any Angle
We can also evaluate trig functions of an angle that contains a point that isn t necessarily on the unit circle. We just need to adjust the trig ratio for the different radius . When given the coordinates of a point on the terminal side of an angle, , in standard position, we can evaluate the six trig functions using these rules:
cos = sec = sin = csc = tan = cot = Where x is the of the point, y is the of the point, and r is the of the circle. radius x-coordinate y-coordinate
You will need to sketch a right triangle and use the theorem to find the length of the radius. Pythagorean
Find the value of the six trigonometric functions of the angle whose terminal side in standard position passes through the given point. If the function is not defined for the angle, state so. ( ) 5. 5, 12
Find the value of the six trigonometric functions of the angle whose terminal side in standard position passes through the given point. If the function is not defined for the angle, state so. ( ) 6. 2, 2
Find the value of the six trigonometric functions of the angle whose terminal side in standard position passes through the given point. If the function is not defined for the angle, state so. Try these on your own! ( ) 4,2 3 7. 0,3 ( ) 8.
We can also use the same rules when given the value of one trig function and the quadrant that it lies in. Use the given to get x, y, and/or r and then use the Pythagorean theorem to find the missing value.
Find the values of the other five trigonometric functions of the angle in the given quadrant having the given function value. sin = 5 13;Q III 9.
Find the values of the other five trigonometric functions of the angle in the given quadrant having the given function value. 10. cos =15 17;Q I
Find the values of the other five trigonometric functions of the angle in the given quadrant having the given function value. 11. csc = 2 3;Q IV
Find the values of the other five trigonometric functions of the angle in the given quadrant having the given function value. 13 2 12. sec = ;Q IV
R x,y ( ) and sin cos Find terminal side of circle and x and y satisfy the given conditions. is the point where the in standard position intersects the unit if 4x = 3y, x 0 13.
R x,y ( ) and sin cos Find terminal side of circle and x and y satisfy the given conditions. is the point where the in standard position intersects the unit if y = x 3, x 0 14.
