Angles Between 90 and 180

Angles Between 90 and 180

Angles on the Cartesian Plan

• an hypotenuse 1 unit long (the radius)

• a side opposite θ that is y units long

• a side adjacent to θ that is x units long

• cos θ = x

• sin θ = y

by symmetry

• sin (180° – θ) = sin θ = y

• cos (180° – θ) = –cos θ = −x

Example 1:

Express each of the following in terms of the same trigonometric ratio of another angle between 0° and 180°. 

• sin 60⁰ = sin (180⁰ - 60⁰) = sin 120⁰

• cos 75⁰ = -cos (180⁰ - 75⁰) = -cos 105⁰

• cos 120⁰ = -cos 60⁰

• sin 150⁰ = sin 30⁰

Example 2:

Use your calculator to determine the all possible values of θ if 0° θ 180°, rounding your answer to the nearest degree. 

•   $\sin\theta=0.3$ ,  $\theta=17.46^0$  or  $\theta=162.54^0$  

•  $\cos\ \theta=0.2$  ,  $\theta=78.46^0$  

•  $\cos\theta=-0.5$  ,  $\theta=120^0$  

•  $\cos\theta=0.5$  ,  $\theta=60^0$  

Multiple Choice

If A is an acute angle, which of the followings is true?

• sin A > 0, cos A < 0

• sin A < 0, cos A > 0

• sin A < 0, cos A < 0

• sin A > 0, cos A > 0

Multiple Choice

If A is an obtuse angle, which of the followings is true?

• sin A > 0, cos A < 0

• sin A < 0, cos A > 0

• sin A < 0, cos A < 0

• sin A > 0, cos A > 0

Multiple Choice

A = 91⁰.

What do we call for angle A?

• Right angle

• Acute angle

• Obtuse angle

• Reflex angle

Multiple Choice

If B = 135⁰, which of the followings is true?

• sin B < 0

• cos B > 0

• cos B < 0

• sin B = 0

Multiple Choice

Which of the followings is true?

• sin 60⁰ = -sin 120⁰

• sin 110⁰ = -sin 70⁰

• cos 50⁰ = cos 130⁰

• cos 160⁰ = -cos 20⁰

Multiple Choice

If sin A = 0.6, which of the following statements is true?

• A is an acute or an obtuse angle

• A is an obtuse angle only

• A is an acute angle only

Multiple Choice

if cos B = 0.7, which of the followings is true?

• B is an acute angle

• B is an obtuse angle

• B is a right angle

Multiple Choice

if cos B = -0.7, which of the followings is true?

• B is an acute angle

• B is an obtuse angle

• B is a right angle

Multiple Choice

Which of the followings is equal to sin 45⁰?

• cos 45⁰

• cos 135⁰

• -sin135⁰

• sin 135⁰

Multiple Choice

Which of the followings is equal to cos 135⁰?

• -cos 45⁰

• cos 45⁰

• -sin135⁰

• sin 45⁰