TRIGONOMETRY

^{0}-Î¸

If Î¸is a reflex angle (180

^{0}< Î¸<270 style="box-sizing: border-box;" sup="">0^{0}

If Î¸is a reflex angle (270

^{0}< Î¸< 360^{0}), then the trigonometrical ratios are the same as that of 360^{0 }-Î¸
We have seen that trigonometrical ratios are positive or negative depending on the size of the angle and the quadrant in which it is found.

The result can be summarized by using the following diagram.

Trigonometric Ratios to Solve Problems in Daily Life

Apply trigonometric ratios to solve problems in daily life

Example 1

Write the signs of the following ratios

- Sin 170
^{0} - Cos 240
^{0} - Tan 310
^{0} - sin 30
^{0}

*Solution*
a)Sin 170

^{0}
Since 170

^{0}is in the second quadrant, then Sin 170^{0 }= Sin (180^{0}-170^{0}) = Sin 10^{0}
∴Sin 170

^{0}= Sin 10^{0}
b) Cos 240

^{0}= -Cos (240^{0}-180^{0)}= -Cos 60^{0}
Therefore Cos 240

^{0}= -Cos 60^{0}
c) Tan 310

^{0 }= -Tan (360^{0}-310^{0}) = - Tan 50^{0}
Therefore Tan 310

^{0}= -Tan 50^{0}
d) Sin 300

^{0}= -sin (360^{0}-300^{0}) = -sin 60^{0}
Therefore sin 300

^{0}= - Sin 60^{0}**Relationship between Trigonometrical ratios**

The above relationship shows that the Sine of angle is equal to the cosine of its complement.

Also from the triangle ABC above

Again using the Î”ABC

b

^{2}= a^{2}+c^{2}(Pythagoras theorem)
And

Example 2

Given thatA is an acute angle and Cos A= 0.8, find

- Sin A
- tan A.

Example 3

If A and B are complementary angles,

*Solution*
If A and B are complementary angle

Then Sin A = Cos B and Sin B = Cos A

Example 4

Given that Î¸and Î²are acute angles such that Î¸+ Î²= 90

^{0}and SinÎ¸= 0.6, find tanÎ²

*Solution*
Exercise 1

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