Name: ____________________
Class / Index: 2I4 ( )
PEER-TEACHING TRIGONOMETRY
Date: _____________
Worksheet
LESSON 1 - TRIGONOMETRIC FUNCTIONS OF ACUTE ANGLES
Note: ALL DIAGRAMS IN THIS WORKSHEET ARE NOT DRAWN TO SCALE
Lesson Objectives:
1. Understand and write three basic trigonometric functions (cosine, sine and tangent) of acute angles using
given sides of the right-angled triangle
2. Find acute angle given trigonometric ratios
3. Solve right-angled triangles using the 3 trigonometric ratios
4. State the trigonometric ratios of the special angles of 30, 45 and 60 degrees.
Introduction
The trigonometric ratios of the sides of right-angle triangles can be found using the 3
functions: sine (sin), cosine (cos) and tangent (tan). On the other hand, the angles of the
right-angle triangles can be found using the 3 functions: 𝑎𝑟𝑐𝑠𝑖𝑛, 𝑎𝑟𝑐𝑐𝑜𝑠 and 𝑎𝑟𝑐𝑡𝑎𝑛.
Remember the functions:
Sin = _____________
Cos = ____________
Tan = ____________
___ ___ ___
-
___ ___ ___
-
___ ___ ___
Prepared by Justin Lo, Lee Bing Qian, Danyon Low, Tan Jing Ling
1
Finding Trigonometric Ratios given Sides of a Triangle
A
𝑥
C
B
Angle 𝒙
Ratio (AC:CB:BA)
Sine
Cosine
Tangent
Example 1:
Find cos 𝑥 :
A
5cm
𝑥
B
4cm
C
Recall the formula:
So:
Prepared by Justin Lo, Lee Bing Qian, Danyon Low, Tan Jing Ling
2
Example 2:
Find tan 𝑥:
A
𝑥
4cm
6cm
B
C
Recall the formula:
So:
Example 3:
Find sin 𝑥:
A
8cm
4.5cm
𝑥
B
C
Recall the formula:
So:
Prepared by Justin Lo, Lee Bing Qian, Danyon Low, Tan Jing Ling
3
Finding Angles with Trigonometric Ratios
Example 1:
Find 𝑥 using 𝑎𝑟𝑐𝑠𝑖𝑛 (to 2 d.p.):
A
6cm
4cm
𝑥
C
B
Recall the formula:
So:
Example 2:
Find 𝑥 using 𝑎𝑟𝑐𝑐𝑜𝑠 (to 2 d.p.):
A
5cm
𝑥
√7cm
B
C
Recall the formula:
So:
Prepared by Justin Lo, Lee Bing Qian, Danyon Low, Tan Jing Ling
4
Example 3:
Find 𝑥 using 𝑎𝑟𝑐𝑡𝑎𝑛 (to 2 d.p.):
A
2cm
𝑥
B
√11cm
C
Recall the formula:
So:
Prepared by Justin Lo, Lee Bing Qian, Danyon Low, Tan Jing Ling
5
More Practices…
1. Circle T if the statement is True or F is the statement is false
a. 𝑠𝑖𝑛, 𝑐𝑜𝑠 and 𝑡𝑎𝑛 only apply to right-angled triangles ---------------- T / F
b. 𝑠𝑖𝑛, 𝑐𝑜𝑠 and 𝑡𝑎𝑛 help one find the lengths of a triangle ------------ T / F
c. The mnemonic is SOH - CAH - TOA ---------------------------------------- T / F
d. sin 30° = cos 60° ------------------------------------------------------------ T / F
e. tan 45° = 1 --------------------------------------------------------------------- T / F
f. 𝑎𝑟𝑐𝑠𝑖𝑛, 𝑎𝑟𝑐𝑐𝑜𝑠 and 𝑎𝑟𝑐𝑡𝑎𝑛 are used to find a ratio ----------------- T / F
g. arcsin 𝑥 = 30° can be rewritten as 𝑠𝑖𝑛 30° = 𝑥 --------------------- T / F
h. arcsin 30° = arccos 60° ---------------------------------------------------- T / F
3
4
5
5
2. Find tan 𝑥 when sin 𝑥 = and cos 𝑥 =
3. If arccos 𝑥 = 30, find 𝑥
4. Find sin 𝑥 :
3
𝑥
4
5. Find 𝑥 using 𝑎𝑟𝑐𝑐𝑜𝑠 (to 2 d.p.):
3
2
𝑥
Prepared by Justin Lo, Lee Bing Qian, Danyon Low, Tan Jing Ling
6