Secant, cosecant and cotangent

1
Secant, cosecant and cotangent
sec 1 . cos
cosec 1 . sin
cot 1 . tan
cos sin
cos²ø sin²ø 1
Divide by cos²ø
cos²ø sin²ø 1 Cos²ø cos²ø cos²ø
1 tan²ø sec²ø
cos²ø sin²ø 1
Divide by sin²ø
cos²ø sin²ø 1 sin²ø sin²ø sin²ø
1 cot²ø cosec²ø
2
Evaluate the following
Sec 60
1 . cos 60
1 . ½
2
1.192
cot 40
1 . tan 40
3
Solve the following
1 4 cos x
Cos x 1 4
x 75.5
Sec x 4
cot x 2
Tan x 1 2
x 26.6
1 2 tan x
4
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
5
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
6
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 cos²Ø tanØ
1 x 1 cos²Ø tanØ
1 x cosØ cos²Ø sinØ
tanØ cotØ tanØ 1 .
tanØ
sec²Ø tanØ
7
Prove the following by putting the stages into
the correct order
Prove tanØ cotØ 1 .
sinØcosØ
tanØ cotØ tanØ 1 .
tanØ
tan²Ø 1 . tanØ
1 cos²Ø tanØ
1 tanØ cos²Ø
sec²Ø tanØ
1 x 1 cos²Ø tanØ
1 x cosØ cos²Ø sinØ
1 . sinØcosØ