Trigonometric Ratios

A

B

C

Trigonometric Ratios

=a

c

A

B

C

a

b

c

=b

c

=a

b

cos A =adjacent

hypotenuse

tan A =opposite

adjacent

hypotenuse

oppositeAsin

Trigonometric Ratios

A

B

C

a

b

c Asin

1A csc

opposite

hypotenuse

a

c

A cos

1A sec

adjacent

hypotenuse

b

c

Atan

1Acot

opposite

adjacent

a

b

Trigonometric RatiosEvaluate the six trigonometric functions of the given angle

8

6

1. 222 cba 26 28 2c

36 264 c2100 c

10c 10

Trigonometric RatiosEvaluate the six trigonometric functions of the given angle

8

6

1.

hypotenuse

oppositeAsin

10

8

5

4

hypotenuse

adjacentθ cos

10

6

5

3

adjacent

oppositeθtan

6

8

3

4

10

sin

1θ csc

4

5

cos

1θ sec

3

5

tan

1θcot

4

3

Trigonometric RatiosEvaluate the six trigonometric functions of the given angle

10

5

2. 222 cba 25 210 2c

25 2100 c2125 c

125c55c 55

Trigonometric RatiosEvaluate the six trigonometric functions of the given angle

Asin 55

10

5

2

θ cos55

5

5

1

θtan 5

102

sin

1θ csc

2

5

cos

1θ sec 5

tan

1θcot

2

1

10

5

2.55

5

52

5

5

Trigonometric RatiosEvaluate the six trigonometric functions of the given angle

4

3

3. 222 cba 23 24 2c

9 216 c225 c

5c 5

Trigonometric RatiosEvaluate the six trigonometric functions of the given angle

Asin 5

3

θ cos5

4

θtan 4

3

sin

1θ csc

3

5

cos

1θ sec

4

5

tan

1θcot

3

4

4

3

3.

5

Trigonometric Ratios

sin

cos

tan

0 30 54 60 90

0

1

0

2

1

2

3

3

3

2

2

2

2

1

2

3

2

1

3

1

0

undef.

Trigonometric RatiosFind the missing side lengths x and y

y30o

4

4. 30sin

x

4

2

1 8x

x

4x

30tan

y

4

3

3

123 y4

y3 3

3

12y

3

312y

33 34y

Trigonometric RatiosFind the missing side lengths x and y

y60o

8

5. 60sin

82

3 x

382 xx

x

8

60 cos82

1 y

82 yy

8 2 24y

2 234x

Trigonometric RatiosFind the missing side lengths x and y

y45o

7

6.

x

45sin

x

7

2

2

7x

142 x2 2

2

14x

22

2

214x

27x

45tan

y

71

7y

7y

Trigonometric Ratios