Download presentation
Presentation is loading. Please wait.
Published byGary Hunt Modified over 9 years ago
1
EXAMPLE 1 Find trigonometric values Given that sin = and < < π, find the values of the other five trigonometric functions of . 4 5 π 2
2
EXAMPLE 1 Find trigonometric values SOLUTION STEP 1 Find cos . Write Pythagorean Identity. sin + cos 2 2 = 1 Substitute for sin . 4 5 ( ) + cos 4 5 2 2 1 = Subtract ( ) from each side. 4 5 2 cos 2 2 4 5 1 – ( ) = Simplify. cos 2 9 25 = Take square roots of each side. cos 3 5 + – = Because is in Quadrant II, cos is negative. cos 3 5 – =
3
EXAMPLE 1 Find trigonometric values STEP 2 Find the values of the other four trigonometric functions of using the known values of sin and cos . tan sin cos == 4 5 3 5 – = 4 3 – cot cos sin = = 4 5 3 5 – = 3 4 –
4
EXAMPLE 1 Find trigonometric values csc sin == 1 4 5 = 5 4 sec cos = = 3 5 – 1 = 5 3 –
5
EXAMPLE 2 Simplify a trigonometric expression Simplify the expression tan ( – ) sin . π 2 Cofunction Identity tan ( – ) sin π 2 cot sin = Cotangent Identity = ( ) ( sin ) cos sin Simplify. = cos
6
EXAMPLE 3 Simplify a trigonometric expression 2 Simplify the expression csc cot +. sin Reciprocal Identity 2 csc cot + sin csc cot + csc 2 = Pythagorean Identity = csc (csc – 1) + csc 2 Distributive property = csc – csc + csc 3 Simplify. = csc 3
7
GUIDED PRACTICE for Examples 1, 2, and 3 Find the values of the other five trigonometric functions of . 1 6 1. cos , 0 < < = π 2 SOLUTION sin = 35 6 sec = 6 csc cot = 6 35 =
8
GUIDED PRACTICE for Examples 1, 2, and 3 Find the values of the other five trigonometric functions of . 2. sin =, π < 3π3π 2 –3 7 SOLUTION cos – = 2 10 7 tan = 20 3 10 csc = 7 3 – sec = – 7 20 10 cot 2 10 3 = –
9
GUIDED PRACTICE for Examples 1, 2, and 3 3. sin x cot x sec x Simplify the expression. 1 ANSWER 4. tan x csc x sec x 1 ANSWER cos –1 π 2 – 1 + sin (– ) 5. –1 ANSWER
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.