Law of sine and cosine

Law of sine and cosine, Radians and Degrees

Practice :)

Degrees and radians

Multiple Choice

Convert 150⁰ to radians

• 5π/6
• 3π/4
• 7π/6
• 2π/3

Multiple Choice

What is  $$225\degree$$   in radians? 

• $$\frac{7\pi}{4}$$  

• $$\frac{5\pi}{4}$$  

• $$\frac{3\pi}{4}$$  

• $$\frac{5\pi}{3}$$  

Law of sines

• sina/A = sinb/B = sinc/C

• Can by ANY triangle (not just right triangle)

Multiple Choice

What is the measure of angle A?

• $$58\degree$$

• $$61\degree$$

• $$78\degree$$

• $$74\degree$$

Multiple Choice

Find the length of Side BC.

• 33

• 24

• 12

• 29

Law of Cosines

Multiple Choice

Find BC

• A
• B
• C
• D

Multiple Choice

Find QR

• 34.7 km
• 2.2 km
• 13.74
• 31.1 km

Law of sine and cosine in context

• DRAW A PICTURE!!

• Label the picture clearly

Multiple Choice

Mr. Creole must find the distance from Point A to Point B on opposite sides of a lake. He locates Point C that is 4.15 miles from point A and 5.33 miles from Point B. He measures the angle ACB to be 37^o. Find the distance from point A to point B.

• 3.72 miles

• 6.18 miles

• 10.30 miles

• 3.21 miles

Multiple Choice

Amanda and Jamie are standing 25 feet apart and spot a bird in the sky between them.  The angle of elevation from Amanda to the bird is 55 degrees, and from Jamie to the bird is 63 degrees.  How far away is the bird from Amanda?

• 25.23
• 23.19
• 22.15
• 20.85

Multiple Choice

Clint is building a wooden swing set for his children.  Each supporting end of the swing set is to be an A-frame constructed with two 10 foot long 4-by-4s joined at a 45 degree angle.  To prevent the swing set form tipping over, Clint wants to secure the base of each A-frame to concrete footings.  How far apart should the footings for each A-frame be?

• 5.461 feet
• 9.743 feet
• 6 feet
• 7.65 feet

Reference angles

• ​Reference angle is the degree from your angle to the x axis.

Multiple Choice

What is the reference angle for 125°?

• 235°

• 125°

• 75°

• 55°

Multiple Choice

What is the reference angle for 275°?

• 85°

• 95°

• -85°

• -95°

Multiple Choice

What is the reference angle for 2pi/3

• pi/4
• 7pi/6
• 4pi/3
• pi/3

​Evaluate trig functions

• ​Graph the angle

• ​Find reference angle

• ​Using 45-45-90 or 30-60-90 triangles to find sides

• ​OR use unit circle

​

​HYPOTENUSE/RADIUS IS ALWAYS 1

Multiple Choice

Evaluate: $$\cos\ \frac{3\pi}{4}$$  

• $$-\frac{1}{\sqrt{3}}$$  

• $$-\frac{\sqrt{2}}{2}$$  

• $$\frac{2}{\sqrt{3}}$$  

• $$\sqrt{2}$$  

Multiple Choice

Evaluate: $$\sec\ 45\degree$$  

• $$\frac{1}{2}$$  

• $$\frac{1}{\sqrt{2}}$$  

• $$\sqrt{2}$$  

• $$\frac{\sqrt{3}}{2}$$  

Multiple Choice

$$\sin0$$  

• 0

• 1

• -1

• undefined

Multiple Choice

$$\tan\frac{3\pi}{2}$$

• 0

• 1

• -1

• undefined

Multiple Choice

Evaluate tan (3π / 4)

• √3 / 2
• 1 / 2
• 1
• 0

Multiple Choice

Evaluate Cos (180)

• 2
• 1
• √2 / 2
• -1