University:
University of North Carolina at Charlotte
Course:
MATH 1242 | Calculus II
Academic year:

2022
Views:

342

Pages:

1
Author:

Rosalinda G

Relating the Trigonometric FunctionsFind the six trigonometric ratios given right triangle.5A817The first step is to make sure you know the adjacent, opposite, and hypotenuse sides of your triangle with respect to the reference angle.The hypotenuse is 17. the side opposite of Ais 8. and the side adjacent to Bis 5.Once your sides have been labeled. you can find each trigonometric ratio by using the appropriate sides.opposite8sin -hypotenusetan 8= o_poste_8adjacentCSC 0 = hypotenuse 17opposite.co_hypotenuse_17sec adjacentoppositecan find a relationship between the labeled angles and their trigonometric be ratios. Since The all the relationships angles intheUsing the same triangle, 180°, you know that 90° + A+ a = 180° Therefore, angles 0 and a must complementary. in the example below.triangle between must complementary add up to angles you play an important role in their trigonometric ratios as is demonstratedsubstituteNotice that sin 0= 8 and COS a = 8 Therefore, sin 0= cos a. Since you know that 0 and a are complementary. you canfind 17 sin A = cos(90°-0). 17 This tells you that the cofunction, or the trigonometric function whose derived value in the is equal same way. to a giventrigonometric a - 90° 0 and function of the complementary angle, of sine is cosine. The other cofunction identities can beKey ConceptCofunction Identitiesan 8 cos(90°-0)cos 8 = sin(90°-8)

Relating the Trigonometric Functions

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