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FINDING THE COORDINATES OF A TRIGONOMETRIC POINTS OF SPECIAL ANGLES Recall that in a 30° -60 -90° triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is 3 times the length of the shorter leg. Example A 30-60-90 Triangle Let us just consider the first quadrant since the triangle is located in the first quadrant. Since the radius of the unit circle is 1, the hypotenuse of the triangle has length 1. Let us call the horizontal side of the triangle x, and the vertical side of the triangle y Since the length of the hypotenuse is 1 and it is twice the length of the shorter leg, y, we can say that y. Since the longer leg. x. 3 tmes the langth of the shorter leg, we can say that x % V3, or equivalenty, Therefore, the coordinate of the point where the teminal side of the |30 angle intersects the unit circle is ( Find the coordinate of the point where the terminal side of the 600 angle intersects the unit circle.

FINDING THE COORDINATES OF A TRIGONOMETRIC POINTS OF SPECIAL ANGLES Recall that in a 30° -60 -90° triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is 3 times the length of the shorter leg. Example A 30-60-90 Triangle Let us just consider the first quadrant since the triangle is located in the first quadrant. Since the radius of the unit circle is 1, the hypotenuse of the triangle has length 1. Let us call the horizontal side of the triangle x, and the vertical side of the triangle y Since the length of the hypotenuse is 1 and it is twice the length of the shorter leg, y, we can say that y. Since the longer leg. x. 3 tmes the langth of the shorter leg, we can say that x % V3, or equivalenty, Therefore, the coordinate of the point where the teminal side of the |30 angle intersects the unit circle is ( Find the coordinate of the point where the terminal side of the 600 angle intersects the unit circle.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.7: Applied Problems
Problem 27E
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FINDING THE COORDINATES OF A TRIGONOMETRIC POINTS OF SPECIAL ANGLES Recall that in a 30° -60° -90° triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is 3 times the length of the shorter leg. 13 Example: A 30° -60° -90° Triangle | Let us just consider the first quadrant since the triangle is located in the first quadrant. Since the radius of the unit circle is 1, the hypotenuse of the triangle has length 1. Let us call the horizontal side of the triangle x, and the vertical side of the triangle y. (x, y) Since the length of the hypotenuse is 1 and it is twice the length of the shorter leg, y, we can say that y =. Since the longer leg, x, is 3 times the length of the shorter leg, we can say that x = % 3, or equivalently, x= Therefore, the coordinate of the point where the terminal side of the 30' angle intersects the unit circle is (,
Transcribed Image Text:FINDING THE COORDINATES OF A TRIGONOMETRIC POINTS OF SPECIAL ANGLES Recall that in a 30° -60° -90° triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is 3 times the length of the shorter leg. 13 Example: A 30° -60° -90° Triangle | Let us just consider the first quadrant since the triangle is located in the first quadrant. Since the radius of the unit circle is 1, the hypotenuse of the triangle has length 1. Let us call the horizontal side of the triangle x, and the vertical side of the triangle y. (x, y) Since the length of the hypotenuse is 1 and it is twice the length of the shorter leg, y, we can say that y =. Since the longer leg, x, is 3 times the length of the shorter leg, we can say that x = % 3, or equivalently, x= Therefore, the coordinate of the point where the terminal side of the 30' angle intersects the unit circle is (,
FINDING THE COORDINATES OF A TRIGONOMETRIC POINTS OF SPECIAL ANGLES Recall that in a 30° -60° -90° triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is 3 times the length of the shorter leg. Example A 30-60-90 Triangle Let us just consider the first quadrant since the triangle is located in the first quadrant. Since the radius of the unit circle is 1, the hypotenuse of the triangle has length 1. Let us call the horizontal side of the triangle x, and the vertical side of the triangle y. Since the length of the hypotenuse is 1 and it is twice the length of the shorter leg. y, we can say that y. Since the longer leg, x. s3 tmes the length of the shorter leg, we can say that x % v3 , or equivalenty, x Therefore, the coordinate of the point where the terminal side of the | 30' angle intersects the unt circle is ( Find the coordinate of the point where the terminal side of the 600 angle intersects the unit circle.
Transcribed Image Text:FINDING THE COORDINATES OF A TRIGONOMETRIC POINTS OF SPECIAL ANGLES Recall that in a 30° -60° -90° triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is 3 times the length of the shorter leg. Example A 30-60-90 Triangle Let us just consider the first quadrant since the triangle is located in the first quadrant. Since the radius of the unit circle is 1, the hypotenuse of the triangle has length 1. Let us call the horizontal side of the triangle x, and the vertical side of the triangle y. Since the length of the hypotenuse is 1 and it is twice the length of the shorter leg. y, we can say that y. Since the longer leg, x. s3 tmes the length of the shorter leg, we can say that x % v3 , or equivalenty, x Therefore, the coordinate of the point where the terminal side of the | 30' angle intersects the unt circle is ( Find the coordinate of the point where the terminal side of the 600 angle intersects the unit circle.
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