Trigonometry Answers

1. An alternating current is given by the formula

I = 30 sin (50 t + 0.26) amps

a) Find the amplitude, periodic time, frequency, and phase angle

b) Find the value of the current at 18ms

c) Find the time at which the current first reaches 20 amps 

d) Plot the curve between 0 and 20ms

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1.f(x)=2 sin (x-​π/​4)

2.f(x)=sin (x+π/​3)

3.f(x)=3 cos (x+π/​6)

4.f(x)=2 cos (x-2π)

5.f(x)=tan x

4 sin 2x sin 6x

A surveyor measured the angle of elevation of a flat spire as from a point on horizontal ground. He moves 30m nearer to the flat and measures the angle of elevation as . Calculate the height of the spire to the nearest hundredth.

The angle at the vertex of a cone is measured using a 30mm diameter coin as shown in the figure below. If the coin lies 3.72mm below the top of the cone, determine the value of angle θ.

Find the solution of the equation in the interval 0⁰ ≤ 𝑥 < 360⁰ 

1. cos x + √𝟑 = - cos x
2. sin² x – tan x cos x = 0 .
3. sin x + √𝟐 = − sin x 
4. 2 cos² x – 5 cos x = 3
5. √𝟑 csc x + 2 = 0

Solve the worded problem:

Example 6-https://ibb.co/41tVQZt

1. Look back at the model in Example 6 on page 7. On which days of the year are there 10 hours of sunlight in Prescott, Arizona?

2. The tide, or depth of the ocean near the shore, changes throughout the day. The depth of the Bay of Fundy can be modeled by:

link model-https://ibb.co/hmrm7GN

where d is the water depth in feet and t is the time in hours. Consider a day in which t = 0 represents 12:00 A.M. At what time(s) is the water depth 3 1/2 feet

1. Is sec (−𝜽) equal to sec 𝜽 or - sec 𝜽? How do you know? 
2. Verify the identity 1 - sin² x cot² x = sin² x. Is there more than one way to verify the identity? If so, tell which way you think is easier and why. 
3. Describe what is wrong with the simplification shown.

cos x - cos x sin² x = cos x - cos x (1 + cos² x)

          = cos x - cos x - cos³ x

          = -cos³ x

4. John said 𝒔𝒊𝒏 𝒙 + 𝒄𝒐𝒔 𝒙 = 𝟐 has no solution. Do you agree with John? Explain why or why not?

Verify identity:

1. 𝒄𝒐𝒕²𝜽+𝟏 / 𝒄𝒐𝒕²𝜽 ≡ 𝒔𝒆𝒄²𝜽 
2.  (𝒄𝒔𝒄²𝜽 − 𝟏)𝒔𝒊𝒏²𝜽≡ 𝒄𝒐𝒔²𝜽
3. 𝟏 − 𝒔𝒆𝒄 𝜶 𝒄𝒐𝒔 𝜶 ≡ 𝒕𝒂𝒏 𝜶 𝒄𝒐𝒕 𝜶 − 1
4. 𝒕𝒂𝒏 𝑨+𝒄𝒐𝒕 𝑨 / 𝒔𝒆𝒄 𝑨 𝒄𝒔𝒄 𝑨 ≡ 1
5. 𝟏 + 𝟐 𝒕𝒂𝒏²𝜽 ≡ 𝒔𝒆𝒄⁴𝜽 − 𝒕𝒂𝒏⁴𝜽

The angle at the vertex of a cone is measured using a 30mm diameter circle. If the circle lies 3.72mm below the top of the cone, determine the value of angle θ.

A surveyor measured the angle of elevation of a flat spire as from a point on horizontal ground. He moves 30m nearer to the flat and measures the angle of elevation as . Calculate the height of the spire to the nearest hundredth. 

Reflect on the concepts of trigonometry. What concepts (only the names) did you need to accommodate the concepts of trigonometry in your mind? What are the simplest trigonometry concepts you can imagine? In your day to day, is there any occurring fact that can be interpreted as periodic patterns? What strategy are you using to get the graphs of trigonometric functions?

Determine the values of x between 0o and 360o for EACH of the following

expressions:

(i) 2 sinx = 1

(ii) tanx = - 0.75 (iii) cosx = sin 5