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• sin 𝜃 cos 𝜃 tan 𝜃•

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𝟏

𝟐𝒂𝒃𝐬𝐢𝐧𝑪

𝑥

𝑎

𝑏

°

𝑎 𝑏𝑎

𝑏

𝑥𝑥

𝑥

𝑥𝑥

𝑎 𝑏

𝑐

𝑎 = 𝑏 =𝑐 =

𝑎 = 𝑏 =𝑐 =

𝑎 =𝑏

𝑐𝑥

𝑥 =

𝑥

4 =𝑥

204 =

20

𝑥2.8 =

5.3

𝑥2.8 =

𝑥

5.3

𝑥

tan 𝜃 =𝑜𝑝𝑝

𝑎𝑑𝑗

tan ? =𝑥

?? × tan ? = 𝑥

? = 𝑥

𝑥 tan 28 =𝑥

3× tan 28 = 𝑥

1.6 = 𝑥

𝑥

tan 31 =?

?𝑥 × tan31 = ?

𝑥 =?

tan 31𝑥

=𝑥 =

𝑦

𝑥.

𝑥

𝑥

√

sin 63.4 =8

4√5

tan 26.6 =4

8

=

sin 𝜃 =

𝑥

sin−1 𝑥 cos−1 𝑥 tan−1 𝑥

sin 𝑥 sin−1 𝑥

tan 𝑥 =?

?𝑥 = tan−1

?

?𝑥 = ?

𝜃

sin 𝜃 = cos𝜃 = tan 𝜃 =

𝜃

= 𝜃

sin 𝜃 =8

10

𝜃 = sin−18

10

𝜃 =

= ==

122 + 52 = 132 62+ ?2 = 100 162 − 122 = ? 2

=

𝑥

𝑥𝑥 °

𝑥

30°, 60° 45°

𝑥 𝑦

√3

𝑥,

sin 𝑥 =?

?=

1

2

sin ? =1

2

𝑥 =

𝑥√

𝑥

𝑥 𝑥

𝑦

𝑦

0°

90°

𝑥

tan 90°

𝑥sin 0 = 0

opp

hyp=

𝑥

𝑥

tan 0 = 0 cos 0 = 1

𝑥

𝑥)

𝑥

𝑥

𝑥

sin 90 = cos 90 = tan 90 =

=

=

=

1

2× ×

=1

2𝑎𝑏 sin 𝐶

=1

2𝑏𝑐 sin𝐴

=1

2𝑎𝑐 sin𝐵

= = √3

𝜃

4𝑥

𝑥

𝜃

ℎ = 𝑎 sin𝐵

ℎ =

𝑎 sin𝐵 =

𝑎

sin ?=

?

sin 𝐵

ℎ𝑏𝑎

𝑡

sin 105=

25

sin ?

sin 𝐶

𝑐

𝑎

sin 𝐴=

𝑏

sin 𝐵

===

𝑎

sin 𝐴=

𝑏

sin 𝐵

sin 𝐴

𝑎=

sin 𝐵

𝑏

𝜃

𝜃

sin 𝜃

3.8=

sin 93

7sin 𝜃 =

sin 93

7

sin 𝜃 =

𝜃 =

𝑎

𝑐

ℎ𝑏

𝑎

𝑐

𝑑 𝑐 − 𝑑

ℎ2 𝑎2 = 𝑏2 + 𝑐2 − 2𝑐𝑑

cos𝐴 =𝑑

𝑏bcos 𝐴 = 𝑑

bcos𝐴 = 𝑑 𝑎2 = 𝑏2 + 𝑐2 − 2𝑐𝑑𝑎2 = 𝑏2 + 𝑐2 − 2𝑏𝑐 cos 𝐴

ℎ2

𝑏 𝑑

ℎ2 = 𝑎2 − (𝑐 − 𝑑) 2

ℎ2 = 𝑎2 − 𝑐2 + 2𝑐𝑑 − 𝑑2

𝑎2 = 𝑏2 + 𝑐2 − 2𝑏𝑐 cos𝐴𝑏2 = 𝑎2 + 𝑐2 − 2𝑎𝑐 cos𝐵

cos𝐶

𝑐

?2 = ?2+ ?2 − 2 × 13 × 11 × cos𝐴= 290 − ? cos𝐴cos𝐴 = 290 − ?

cos 𝐴 =?

?𝐴 = cos−1 ?

cos𝐴

B

= °= °

𝑏𝜃 𝜃

=