7/31/2019 Worked Solutions to Class Handout Trig Topic 4

1/15

Worked solutions to Class

Handout Trig Topic 4

(Trigonometric Ratios KNOW THIS

for Fridays Quiz!!!)

7/31/2019 Worked Solutions to Class Handout Trig Topic 4

2/15

x-coordis

or

(principal

angle)

y-coordis

y-coordis

x-coordis

or

(principal

angle)

y-coordis

y-coordis

=

=

=

=

=

=

(reciprocal of

)

or

(principal

angle)

7/31/2019 Worked Solutions to Class Handout Trig Topic 4

3/15

x-coordis

y coord (opp)

y-coordis

=

x-coordis

y-coordis

x-coordis

y-coordis

=

x coord (adj)

y

x

x coord (opp)

= /

=

y coord (adj)

y coord

=

=

x coord

SAME POINT as

last question!

(coterminal)

7/31/2019 Worked Solutions to Class Handout Trig Topic 4

4/15

optional covert to

degrees

or

Quad III

Use CALCULATOR!

Same answerif we work in

degrees, approximately .

Principal angle

is 65

=

()

Secantis the reciprocal of cosine

so approximately .

This is radians convert to

degrees.

Degrees

Principal

Angle

Quad I

Quad IV

cotangentis the reciprocal of

tangent so approximately .

(we could also have used the rotation

angle of1002.7)

7/31/2019 Worked Solutions to Class Handout Trig Topic 4

5/15

Where on the unit circle is the

y-coord (sine!) equal to

?

Where on the unit circle is the

x-coord (cosine!) equal to

?

Where on the unit circle is the

y-coord (sine!) equal to

?

=

Re-write in terms of

sine, knowing that sin

is the reciprocal ofcsc

=

=

=

Alternate Solution:

Use inverse sine (in degree mode) to get the reference

angle, here 30. Then, use CAST rule to determine that

sine is positive in Quads I and II, so the second solution is180-30. Then convert and to radians!

7/31/2019 Worked Solutions to Class Handout Trig Topic 4

6/15

Where on the unit circle is the

y-coord (sine!) equal to

?

This is NOT a standard unit

circle point! (use calculator)

Where is y-coord0.666..?

(Approximate) Solutions in DEGREES:

..(Approximate) Solutions in DEGREES:

Where on the unit circle is the

x-coord (cosine!) equal to ?

=

,

Use CALC for tan equations.

TAN is POS (+) in Quads I and III

TAN is positive in Quads I and III

=

,

7/31/2019 Worked Solutions to Class Handout Trig Topic 4

7/15

=

Re-write in terms of

sine, knowing that sin

is the reciprocal ofcsc

Where is y-coord -0.5?

=

,

NO SOLUTIONS, the

maximum cosine (or

sine) can be is 1

NOT a standard unit

circle ratio! (Use Calc)

In DEGREES.

In RADIANS.

..

7/31/2019 Worked Solutions to Class Handout Trig Topic 4

8/15

(Pythagorean Theorem)

reference angle

=

=

=

=

=

=

. rads

Find reference angle: Again in RADIAN mode:

Since is in Quad IV:

7/31/2019 Worked Solutions to Class Handout Trig Topic 4

9/15

Done in class: is in Quad III, =

or

=

OPP

HYP

sec is positive where cos is positive

(Quads I and IV) Since sine is negative, is in QUAD IV

(Pythagorean Theorem)

=

Find reference angle:

Again in RADIAN mode:

Since is in Quad IV:

. rads

7/31/2019 Worked Solutions to Class Handout Trig Topic 4

10/15

+ =

(.)+ =

= .

= .

= . .

.

= .

=

=

=

=

=

=

=

y

x

=

=

7/31/2019 Worked Solutions to Class Handout Trig Topic 4

11/15

Quadrant III =

Reciprocal:

opp

hyp

(Pythagorean Theorem)

=

For tangent, fined the adj side, (pyth. theorem), then use the ratio =

opp

adj

=

7/31/2019 Worked Solutions to Class Handout Trig Topic 4

12/15

is the -coord, or

=

=

is the -coord, or

=

= +

=

+

+

7/31/2019 Worked Solutions to Class Handout Trig Topic 4

13/15

=

opp

adj

is positive in QUADS I and III

(since we want the largest positive

angle, well focus on the QUAD IIIangle)

=

Since is in quad III, well make the opp,

adj sides both negative.

Find reference angle

Again in RADIAN mode

Since is in Quad IV

248 .rads

7/31/2019 Worked Solutions to Class Handout Trig Topic 4

14/15

Difference=

=

=

Alternate solution: Convert to degrees,

subtract, then convert back to radians.

7/31/2019 Worked Solutions to Class Handout Trig Topic 4

15/15