Determine whether the statement is true or false.
sin x(csc x−cot x)=1−cos x [7.1]
sin 42°=1+cos 84°2−−−−−−−−−−√ [7.2]
sin π9=cos 7π18 [7.2]
cos2 x≠cos x2 [7.1]
For Exercises 5–14, choose one of expressions A–J to complete the identity. [7.1], [7.2]
-
-
-
-
-
-
-
-
-
cos x2=
2 sin x cos x
±1+cos x2−−−−−−−−√
csc2 x
2 tan x1−tan2 x
±1−cos x2−−−−−−−−√
sec x
sin u cos v−cos u sin v
cos u cos v−sin u sin v
cot x
cos x
cot xsin x−−−−−√ [7.1]
1sin2 x−(cos xsin x)2 [7.1]
2 cos2 x−5 cos x−3cos x−3 [7.1]
sin xtan (−x) [7.1]
(cos x−sin x)2 [7.2]
1−2 sin2 x2 [7.2]
Rationalize the denominator:
sec x1−cos x−−−−−−−−√. [7.1]
Write cos 41° cos 29°+sin 41° sin 29° as a trigonometric function of a single angle and then evaluate.[7.1]
Evaluate cos 3π8 exactly.[7.1]
Evaluate sin 105° exactly.[7.1]
Assume that sin α=513 and sin β=1213 and that α and β are between 0 and π/2, and evaluate tan (α−β).[7.1]
Find the exact value of sin 2θ and the quadrant in which 2θ lies if cos θ=−45, with θ in quadrant II.[7.2]
Prove the identity. [7.3]
cos2 x2=tan x+sin x2 tan x
1−sin xcos x=cos x1+sin x
sin3 x−cos3 xsin x−cos x=2+sin 2x2
sin 6θ−sin 2θ=tan 2θ(cos 2θ+cos 6θ)
Collaborative Discussion and Writing
Explain why tan (x+450°) cannot be simplified using the tangent sum formula, but can be simplified using the sine and cosine sum formulas. [7.1]
Discuss and compare the graphs of y=sin x, y=sin 2x, and y=sin (x/2). [7.2]
What restrictions must be placed on the variable in each of the following identities? Why? [7.3]
a) sin 2x=2 tan x1+tan2 x
b) 1−cos xsin x=sin x1+cos x
Find all errors in the following:
2 sin2 2x+cos 4x
===2(2 sin x cos x)2+2 cos 2x8 sin2 x cos2 x+2(cos2 x+sin2 x)8 sin2 x cos2 x+2.
[7.2]
..................Content has been hidden....................
You can't read the all page of ebook, please click
here login for view all page.