Trigonometry Answers

Two points X and Y, 1000 m apart are located on a straight road running east and west. From

X, the bearing of a tower is 32°W of N and from Y the bearing of the town 26° N of E. Determine

the shortest distance of the tower from the road.

Suppose we have two numbers x and y whose difference is 8 and x is less than y

1.1. Find the function that models the number y in terms of the number x

1.2. Find the function that models the sum S of the squares of the two numbers in terms of x

1.3. Determine the values of the two numbers such that S is a minimum. Include the steps of your reasoning

2.1. Prove the identity 1/(1-sinθ) =sec²θ+tanθ.secθ

2.2. For which values of θ is the identity in 2.1. undefined?

2.3. Solve the equation 2cos 2x.cosec²x=2cos 2x for x"\\isin" (-π ,"\\pi" )

3.1. Use the special triangles and the additional formula for sine to determine the value of sin 75°. Leave the answer in surd form if necessary

3.2. Suppose we have a triangle ABC where angle ABC is equals to 75°, angle BAC is equals to 60° and the length of AC is equals to 10 cm

(i) Briefly sketch the triangle, displaying all the given information

(ii) Use the Law of Sines, and yours answer in 3.1. to determine the length of AB. Leave the answer in surd form if necessary

Prove that

(a) (sin x + cos x) (tan x + cot x) = sec x + cosec x.

(b) sec x sin x / tan x + cot x = sin² x .

Prove that cos 3theta - cos theta/sin 3 theta sin theta = 4 cos theta/ 1- 4 cos^2 theta

Given that y

 = 11 cm and θ

 = 44°, work out x

 rounded to 1 DP.

The bearing of a lighthouse from ship A is N29°E and the bearing of that lighthouse from ship B is N61°W. If ship A and ship B are on the east-west line 200 kilometers apart, how far is ship B from the lighthouse?

Two light spotted the same mark on the tower, the mark was 36 ft. from the ground. The first light forming 97 ft. ray and 20º angle from the ground and the second one nearer to the mark was 70 ft. from the first. Find the length of the ray from the second light to the mark

graph the expression 1-tan^2x/1+tan^2x, and make a conjecture about another expression that is equivalent to another.