: Find the values of the six trigonometric functions for θ. Special Right Triangles:

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1 ALGEBRA 2 CHAPTER 13 NOTES Section 13-1 Right Triangle Trig Understand and use trigonometric relationships of acute angles in triangles. 12.F.TF.3 CC.9- Determine side lengths of right triangles by using trigonometric functions. CC.9-12.F.TF.5 A function is a function whose rule is given by a trigonometric ratio. A compares the lengths of two sides of a right triangle. The Greek letter theta is traditionally used to represent the measure of an acute angle in a right triangle. SOH-CAH-TOA Find the values of the six trigonometric functions for θ. 70 Special Right Triangles: : 24

2 : Use a trigonometric function to find the value of x. A skateboard ramp will have a height of 12 in., and the angle between the ramp and the ground will be 17. To the nearest inch, what will be the length l of the ramp? When an object is above or below another object, you can find distances indirectly by using the or the between the objects.

3 ALGEBRA 2 CHAPTER 13 NOTES Section 13-2 Angles Draw angles in standard position. Determine the values of the trigonometric functions for an angle in standard position. An angle is in when its vertex is at the origin and one ray is on the positive x-axis. The of the angle is the ray on the x-axis. The other ray is called the of the angle. Positive Angles: Negative Angles: Draw an angle with the given measure in standard position are angles in standard position with the same terminal side. Find the measures of a positive angle and a negative angle that are coterminal with each given angle. θ = 65 θ = 410

4 For an angle θ in standard position, the is the positive acute angle formed by the terminal side of θ and the x-axis. Find the measure of the reference angle for each given angle. θ = 135 θ = 105 θ = 325 Putting an angle on the xy-axis. P( 3, 6) is a point on the terminal side of θ in standard position. Find the exact value of the six trigonometric functions for θ.

5 ALGEBRA 2 CHAPTER 13 NOTES Section 13-3 Radian Measure and Unit Circle Convert angle measures between degrees and radians. Find the values of trigonometric functions on the unit circle. So far, you have measured angles in degrees. You can also measure angles in. A is a unit of angle measure based on arc length. Recall from geometry that an is an unbroken part of a circle. If a central angle θ in a circle of radius r, then the measure of θ is defined as 1 radian The circumference of a circle of radius r is. Converting from degrees to radians: Converting from radians to degrees: A is a circle with a radius of 1 unit. For every point P(x, y) on the unit circle, the value of r is 1. Therefore, for an angle θ in the standard position: How to determine the values of a trig function on a Unit Circle: 1. Draw the Angle on the xy plane 2. Determine the reference angle. 3. Construct a triangle with the x-axis and label the sides ( or ). 4. Calculate using the appropriate trig ratio.

6 Another way to express the trigonometric functions: Use a reference angle to find the exact value of the sine, cosine, and tangent of each angle 30

7 y = sin θ ALGEBRA 2 CHAPTER 13 NOTES Section 13-3 Quadrantal Angles Construct basic sine, cosine and tangent graphs Calculate the values of the Quadrantal Angles y = cos θ y = tan θ sin 270 cos 90 tan π 2 csc π

8 ALGEBRA 2 CHAPTER 13 NOTES Section 13-4 Inverse Trig Functions Evaluate inverse trigonometric functions. Use trigonometric equations and inverse trigonometric functions to solve problems. You have evaluated trigonometric functions for a given angle. You can also find the measure of angles given the value of a trigonometric function by using an relation. 1 3 Find all of the possible values of the function: cos 2 Find all of the possible values of the function: tan 1 ( 1) Principal Values of Inverse Trig Functions y = Sin 1 x y = Cos 1 x y = Tan 1 x Evaluate each inverse trigonometric function. Give your answer in both radians and degrees Cos 1 ( 3 2 ) Arctan( 1) Sin 1 ( 2 2 ) Cos 1 (0)

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10 ALGEBRA 2 CHAPTER 13 NOTES Section 13-5 Law of Sines Determine the area of a triangle given side-angle-side information. Use the Law of Sines to find the side lengths and angle measures of a triangle. Find the area of the triangle. Round to the nearest tenth. Solve the triangle. Round all values to the nearest tenth.

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12 ALGEBRA 2 CHAPTER 13 NOTES Section 13-6 Law of Cosines Use the Law of Cosines to find the side lengths and angle measures of a triangle. Use Heron s Formula to find the area of a triangle. Law of Cosines: Use the given measurements to solve ABC. Round to the nearest tenth. a = 8, b = 5, m C = 32.2 a = 35, b = 42, c = 50.3