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Trigonometry
1. Evaluate the following:
a. Cos 118°
b. Sin 135°
c. Tan 252°
d. Sin (-60°)
e. Tan (-148°)
2. Determine the following ratios:
a. Sin 850°
b. Cos 920°
c. Tan 1040°
a. Cos 118°
b. Sin 135°
c. Tan 252°
d. Sin (-60°)
e. Tan (-148°)
2. Determine the following ratios:
a. Sin 850°
b. Cos 920°
c. Tan 1040°
Trigonometry
In a triangle, suppose A=37∘, a=3, and b=4.
Find B, C, and c.
SHOW ALL WORK TO RECEIVE FULL CREDIT
If there are no solutions, show why and then write NO SOLUTIONS as your final answer.
If there are two solutions, find B1, C1, and c1
and then find B2, C2, and c2
.
Trigonometry
Find all solutions in [0,2π) to the equation
2sin2(A)=cos(A)+1
SHOW ALL WORK
Trigonometry
Suppose sin(A)=3/5 and A is in Q2, and cos(B)=−5/13 and B is in Q3. Find the exact value of cos(A+B).
SHOW ALL WORK
Trigonometry
A ladder AB which is setup with B on the horizontal ground and A against a vertical wall, makes an angle of 71 degrees with the ground. it is prevented from slipping by a tight rope PQ of length 1.68 metres, fixed at P to the foot of the wall and at Q to the ladder, PQ being at right angles to AB. Calculate in centimetres
a) The height AP of the ladder above P
b) The length of the ladder?
a) The height AP of the ladder above P
b) The length of the ladder?
Trigonometry
4. (a) Suppose a particle P is moving in the plane so that its coordinates are given by P(x,y), where x = 4cos2t, y = 7sin2t.
(i) By finding a, b ∈ R such that x^2/a^2+y^2/ b^2 = 1, show that P is travelling on an elliptical
path.
(ii) Let L(t) be the distance from P to the origin. Obtain an expression for L(t).
(iii) How fast is the distance between P and the origin changing when t = π/8?
(i) By finding a, b ∈ R such that x^2/a^2+y^2/ b^2 = 1, show that P is travelling on an elliptical
path.
(ii) Let L(t) be the distance from P to the origin. Obtain an expression for L(t).
(iii) How fast is the distance between P and the origin changing when t = π/8?
Trigonometry
prove that
(2cosθ−1)(2cosθ−1)(2cos2θ−1)=2cos4θ+1
(2cosθ−1)(2cosθ−1)(2cos2θ−1)=2cos4θ+1
Trigonometry
Express Sin Cos y 8 6 in the form rSin y , where is an acute angle in
degrees.
degrees.
Trigonometry
If n is a positive integer, prove that (√3+1)^n +(√3-1)^n = 2^n+1 cosπn/6
Trigonometry
Prove that (1+costheta+isintheta)^n + (1+costheta-isintheta)^n =2^n+1 cos^n π/2 cosntheta/2
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#340153 on Dec 2023
#340153 on Dec 2023