Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Pre-Calculus Section 6.1 Using Fundamental Identities Review identities on p. 498. Use the given values to evaluate (if possible) the remaining trigonometric functions. 1. sin x 1 , cos x 3 2 2 2. tan x 7 , sec x 25 24 24 3. tan x = 2, sin x < 0 4. sin x 2 , tan x 2 5 5 3 Match the trigonometric expression with one of the following. (a) –tan x (e) -1 (b) tan x (f) sec2x 1. secx cosx 2. cot2x – csc2x 3. sin x cos x 4. sinx secx 5. sec4x – tan4x 6. sec2 x 1 sin 2 x (c) 1 (d) sec2 x + tan2 x Use the fundamental identities to simplify the expression. Use the table feature of a graphing calculator to check your result numerically. 1. cotx sinx 2. sinφ(cscφ – sinφ) 3. csc x cot x Verify the identity algebraically. 1. sin x + cos x cot x = csc x 2. 1 cos sin 2csc 1 cos sin 3. csc x tan x = sec x 4. cot( ) cos csc Factor the expression and use the fundamental identities to simplify. 1. cot2 x – cot2 x cos2 x 3. sin4x – cos4x 2. tan4 x + 2tan2 x + 1 Perform the indicated operations and use the fundamental identities to simplify. 1. (sin x + cos x)2 2. (csc x + 1)(csc x – 1) 3. 1 1 1 cos x 1 cos x 4. 2 tan x sec x tan x Rewrite the expression so that it is not in fractional form. 1. sin 2 1 cos HW: p. 503-504 2-72 even 2. 3 sec x tan x