cot (90-q) answer the question
Answers
Answer:
cos (90° - θ) = OFOE
cos (90° - θ) = DCOC, [OF = DC and OE = OC, since ∆EOF ≅ ∆COD]
cos (90° - θ) = sin θ
tan (90° - θ) = FEOF
tan (90° - θ) = ODDC, [FE = OD and OF = DC, since ∆EOF ≅ ∆COD]
tan (90° - θ) = cot θ
Similarly, csc (90° - θ) = 1sin(90°−Θ)
csc (90° - θ) = 1cosΘ
csc (90° - θ) = sec θ
sec ( 90° - θ) = 1cos(90°−Θ)
sec (90° - θ) = 1sinΘ
sec (90° - θ) = csc θ
and cot (90° - θ) = 1tan(90°−Θ)
cot (90° - θ) = 1cotΘ
cot (90° - θ) = tan θ
Solved examples:
1. Find the value of cos 30°.
Solution:
cos 30° = sin (90 - 60)°
= sin 60°; since we know, cos (90° - θ) = sin θ
= √32
2. Find the value of csc 90°.
Solution:
csc 90° = csc (90 - 0)°
= sec 0°; since we know, csc (90° - θ) = sec θ
= 1
● Trigonometric Functions
cot
(
90
)
=
0
Explanation:
Recall that
cot
(
θ
)
=
1
tan
(
θ
)
and that
tan
(
θ
)
=
sin
(
θ
)
cos
(
θ
)
So,
cot
(
θ
)
=
1
tan
(
θ
)
=
1
sin
(
θ
)
cos
(
θ
)
=
cos
(
θ
)
sin
(
θ
)
Now, let's just put in 90 degrees for
θ
cot
(
θ
)
=
cos
(
θ
)
sin
(
θ
)
cot
(
90
)
=
cos
(
90
)
sin
(
90
)
Recall, from the unit circle (below) that
sin
(
90
)
=
1
and
cos
(
90
)
=
0
:
enter image source here
So,
cot
(
90
)
=
cos
(
90
)
sin
(
90
)
cot
(
90
)
=
0
1
=
0Answer if you like mark me brainlest