U8 Solving Trig Equations

Evaluating/Restrictions

100

Do we restrict the range when EVALUATING trig expressions?

Yes! We restrict the range when evaluating (not solving) to find ONE solution.  It's either restricted between [-90,90] or [0,180] depending on the function.

200

What is the range restriction for evaluating cosine?

[0,180] degrees

300

What is the range restriction for evaluating cosecant?

[-90,90] degrees

400

What is the range restriction for evaluating cotangent?

[0,180] degrees

500

What is the range restriction for evaluating sine?

[-90,90] degrees

Let's Evaluate!

100

Evaluate:  sec^-1(-2)=

Remember to restrict the range (meaning you should only have ONE answer).  Give your answer in degrees AND radians.  Hint: sec is cos upside down

120 degrees or 2pi/3

200

Evaluate:  sin^-1 (-root2/2)=

Remember to restrict the range (meaning you should only have ONE answer).  Give your answer in degrees AND radians.  Hint:  sin is the y-value

-45 degrees or -pi/4

300

Evaluate:  cot^-1(root3/3)=

Remember to restrict the range (meaning you should only have ONE answer).  Give your answer in degrees AND radians.  Hint:  cot is x/y

30 degrees or pi/6

400

Evaluate:  cos(csc^-1(2))=

Hint: work from the inside out.  Your answer will be a SIDE ratio

root3/2

500

Evaluate:  cos(arctan(-1))=

Hint: work from the inside out.  Your answer will be a side ratio.

root2/2

Using Triangles

100

Find the exact value of the following by drawing a triangle to help you.

tan(sec^-1(5/4))=

Hint: your answer will be a side ratio

3/4

200

Find the exact value of the expression by drawing a triangle to help you.

cos(csc^-1(5/2))=

root21/5

300

Find the exact value of the expression by drawing a triangle to help you.

sec(sin^-1(14/50))=

25/24 (reduced from 50/48)

400

Find the exact value by drawing a triangle to help you.

sin(sec^-1(7/5))=

2root6/7 (root 24 is simplified to 2root6)

500

Find the exact value of the expression by drawing a triangle to help you.

csc(cos^-1(6/13))=

13root133/133 (rationalized version of 13/root133)

Linear Equations

100

Do we restrict the range when SOLVING trig equations?

No!  We find all possible answers in the unit circle.

200

Solve over the interval [0,360].

2-4tanx=2

x=0 and 180 degrees

300

Solve over the interval [0,360].

4-4secx=12

x= 60 and 300

400

Solve over the interval [0,360].

2+secx=-1-2secx

x=180

500

Solve over the interval [0,360].

6-3cscx=2root3+6

x=300 and 210 degrees

Factoring Equations

100

Solve over the interval [0,360].

tanx+root2tanxsinx=0

x = 0 and 180 and 225 and 315

200

Solve over the interval [0,360].

root3sinxcscx+cscx=2sinx+cscx

x = 0, 180, 60, 120 degrees

300

Solve over the interval [0,2pi].

-3tan²x+1 = -2tan²x

pi/4 and 3pi/4 and 5pi/4 and 7pi/4

400

Solve over the interval [0,2pi].

2cos²x-1=0

x = pi/4, 3pi/4, 5pi/4, 7pi/4

500

Solve over the interval [0,2pi].

2sin²x-3sinx=-1

x = pi/6, 5pi/6, pi/2