Problems
Problem :
Solve the following equation:
cos(x) - tan2(x) = 1
.
Using the identity
1 + tan2(x) = sec2(x)
, the equation
cos3(x) = 1
results. Therefore
cos(x) = 1
, and
x = 0
.
Problem :
Solve the following equation:
2 sec(x)sin3(x) = cos(x)tan2(x)
.
Resolving everything into sines and cosines and then cancelling, we have
sin(x) =
.
x =
,
.
Problem :
Calculate
cos(15)
using the fact that
cos(30) =
.
Problem :
θ
is in the first quadrant, and
tan(θ) =
. Find
the sine, cosine, and tangent of
2θ
.
sin(θ) =
.
cos(θ) =
. With these
values, we can calculate sine, cosine, and tangent of
2θ
.
sin(2θ) = 2 sin(θ)cos(θ)
0.4283.cos(2θ) = cos2(θ) - sin2(θ)
-0.9036.tan(2θ) =
- 0.4740
.
Problem :
Express the following as a function of a single angle:
.
Problem :
Express the following as a sum or difference:
cos(100)cos(50)
.
cos(100)cos(50) =
(cos(100 + 50) + cos(100 - 50)) =
(cos(150) + cos(50)
.
Problem :
Simplify:
sin2(x) + cos2(x) - sec2(x) + tan2(x)
.
sin2(x) + cos2(x) - sec2(x) + tan2(x) = 0
.
Problem :
Solve:
cos(x)tan(x) = csc2(x) - cot2(x) - 1
.
x = {0,
, Π,
}