Transcript Secant, cosecant and cotangent

Secant, cosecant and cotangent
sec =
1 .
cosec = 1 .
cos
sin
cos²ø + sin²ø ≡ 1
cos²ø + sin²ø ≡
cot = 1 .
tan
Divide by cos²ø
1
1 + tan²ø ≡ sec²ø
Cos²ø cos²ø cos²ø
cos²ø + sin²ø ≡ 1
cos²ø + sin²ø ≡
sin²ø
sin²ø
Divide by sin²ø
1
sin²ø
1 + cot²ø ≡ cosec²ø
= cos
sin
Evaluate the following
Sec 60° = 1 . = 1 .
cos 60°
½
cot 40°
= 1 .
tan 40°
= 1.192
=2
Solve the following
Sec x = 4
cot x = 2
1 =4
cos x
1
tan x
=2
x = 75.5 °
Cos x = 1
4
Tan x = 1
2
x = 26.6°
Prove the following by putting the stages into the correct
order
Prove (sinØ + cosØ)² - 2sinØcosØ = 1
sin²Ø + cos²Ø ≡ 1
(sinØ + cosØ) (sinØ + cosØ) - 2sinØcosØ
sin²Ø + 2sinØcosØ + cos²Ø - 2sinØcosØ
Prove the following by putting the stages into the correct
order
Prove (sinØ + cosØ)² - 2sinØcosØ = 1
(sinØ + cosØ) (sinØ + cosØ) - 2sinØcosØ
sin²Ø + 2sinØcosØ + cos²Ø - 2sinØcosØ
sin²Ø + cos²Ø ≡ 1
Prove the following by putting the stages into the correct
order
Prove tanØ + cotØ =
1 .
sinØcosØ
tan²Ø + 1 .
tanØ
1 ÷ tanØ
cos²Ø
1 .
sinØcosØ
1
x cosØ
cos²Ø
sinØ
1
cos²Ø
tanØ
tanØ + cotØ = tanØ +
1 .
tanØ
1
x
1
cos²Ø
tanØ
sec²Ø
tanØ
Prove the following by putting the stages into the correct
order
Prove tanØ + cotØ =
1 .
sinØcosØ
tanØ + cotØ = tanØ +
sec²Ø
tanØ
1
x
1
cos²Ø
tanØ
1 .
tanØ
1
cos²Ø
tanØ
tan²Ø + 1 .
tanØ
1 ÷ tanØ
cos²Ø
1
x cosØ
cos²Ø
sinØ
1 .
sinØcosØ