Ratios and Graphs of Trigonometric Functions

Question 13: Which of the following graph represents y = tan x for 0o ≤ x ≤ 360o?     Solution: Answer: A Question 14: Which graph represents part of y = tan x?   Solution: Answer: C

Question 10: Which of the following graph represents y = cos 2x?   Solution: Answer: C Question 11: Which of the following graph represents y = cos x for 0o ≤ x ≤ 180o?   Solution: Answer: D Question 12: Which graph represents part of y = cos x?   Solution: Answer: B

Question 7: Which graph represents y = sin x for 0o ≤ x ≤ 270o?   Solution: Answer: B Question 8: Which graph represents y = sin x for 0o ≤ x ≤ 180o? Solution: Answer: D Question 9: Which graph represents part of y = sin x?     Solution: Answer: A

Question 4: In the diagram above, WZY  is a straight line.  ∠ X Y Z = 90 o , ∠ X W Z = 30 o and WZ = XZ = 30 cm. Find the length of XY. Solution: ∠WXZ=∠XWZ= 30 o ∴∠XZY= 30 o + 30 o = 60 o sin∠XZY= XY XZ sin … Read more

Question 1: In the diagram above, find the value of tan θ. Solution: In △ A B C , using Pythagoras’ Theorem, A C = 1 2 + 1 2 = 2 c m tan θ = C D A C tan θ = 1 2 Question 2: In the diagram above, ABCE is a … Read more

6.2 Graphs of Sine, Cosine and Tangent   (1)  y = sin x, 0o ≤ x ≤ 360o   x 0o 90o 180o 270o 360o sin x 0 1 0 -1 0   (2)  y = cos x, 0o ≤ x ≤ 360o   x 0o 90o 180o 270o 360o cos x 1 0 -1 … Read more

(A) Special Angle (B) Finding the Angles between 0oand 360o Given Values of sin θ, cos θ or tan θ   1. If the value of sin θ, cos θ or tan θ is given and 0o< θ < 360o, the value of θ can be found using the following steps. (a) Find the basic … Read more

6.1 Values of Sine, Cosine and Tangent of an Angle (A) Sine, Cosine and Tangent for Right-Angled Triangles   sin θ = opposites side hypotenuse cos θ = adjacent side hypotenuse tan θ = opposites side adjacent side (B) Values of Sin θ, Cos θ and Tan θ in First Quadrant of the Unit Circle … Read more