Trigonometric Homework

Trigonometry  is a branch of mathematics that studies triangles, particularly right triangles. Trigonometry deals with relationships between the sides and the angles of triangles, and with trigonometric functions, which describe those relationships and angles in general, and the motion of waves such as sound and light waves.(Source : WIKIPEDIA)

Understanding real life applications of trigonometry is always challenging for me but thanks to all math help websites to help me out.

Trigonometric Homework topics:

The trigonometric homework includes the following topic.

• Trigonometric Functions
• Trigonometric Ratio
• Trigonometric Ratios
• Trigonometric Identities
• Supplementary Angles
• Complementary Angles
• Trigonometric Tables
• Trigonometry Equations
• Pythagoras' Theorem
• Right angle triangle

    Let us see some sample homework problems and methods to solve those problems.

Solved Trigonometric homework problems:

Example 1:
Solve by simplification:  cos⁴ `theta`   + cos ²`theta`sin ²`theta`

Solution:

Given cos⁴  `theta`+ cos ²`theta` sin ²`theta`
Factor cos⁴  `theta`  = (cos ²`theta` )(cos ²`theta` )
cos⁴ `theta`+ cos ²`theta` sin ²`theta`=(cos ²`theta` )(cos ²`theta`) + cos ²`theta` sin ²`theta`
(cos ²`theta` ) is common in both term.So take it out.
 = cos ²`theta` (cos ²`theta`  + sin ²`theta` )
 =  cos ²`theta`           { Formula : cos ²`theta`  + sin ²`theta` = 1}
Answer :cos⁴ `theta` + cos ²`theta` sin ²`theta`cos ²`theta` 
Example 2:
Solve by using Pythagoras' Theorem:
Find the x value for the following figure.

Fig (i) Right angle triangle

Solution:
Given AB =3 and AC = 4.
According to the Pythagoras' Theorem,
AB² + AC² = BC²
3² + 4² = x²
9 + 16 = x²
25 = x²
x² = 25
Taking square root on both side,
`sqrt(x^2)``sqrt(25)`
x = 5
Example 3:
Solve by simplification
cos (- x) sin (`Pi / 2` - x)

Solution:

Given cos (- x) sin (`Pi / 2` - x)

 We know that cos (- x)  = cos (x)
                          sin (`Pi / 2` - x) = cos (x)
 cos (- x) sin (`Pi / 2` - x)  = cos(x) cos (x) 
                              = cos²(x)
Answer: cos (- x) sin (`Pi / 2` - x) = cos²(x)


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Example 4:
Find  trigonometric ratios of sin , cos ,tan for the below figure.

Solution:
We know that,


sin x = 4/5 =0.8
Cos x = 3/5 = 0.6
tanx = 4/3 =0.33