Find the six function values of 8^circ in terms of p, q and r, if sin82^circ=p cos82^circ=q tan82^circ=r

Question
Analytic geometry
asked 2020-11-08
Find the six function values of \(\displaystyle{8}^{\circ}\) in terms of p, q and r, if
\(\displaystyle{{\sin{{82}}}^{\circ}=}{p}\)
\(\displaystyle{{\cos{{82}}}^{\circ}=}{q}\)
\(\displaystyle{{\tan{{82}}}^{\circ}=}{r}\)

Answers (1)

2020-11-09
Recall that,
\(\displaystyle{c}{s}\otimes={\sin{{\left({90}^{\circ}-{x}\right)}}},\)
\(\displaystyle{\sin{{x}}}={\cos{{\left({90}^{\circ}-{x}\right)}}},\)
\(\displaystyle{\cot{{x}}}={\tan{{\left({90}^{\circ}-{x}\right)}}},\)
\(\displaystyle{\tan{{x}}}={\cot{{\left({90}^{\circ}-{x}\right)}}},\)
Therefore,
\(\displaystyle{{\sin{{8}}}^{\circ}=}{{\cos{{82}}}^{\circ}}\)
\(\displaystyle{{\sin{{8}}}^{\circ}=}{q}\)
\(\displaystyle{{\cos{{8}}}^{\circ}=}{{\sin{{82}}}^{\circ}}\)
\(\displaystyle{{\cos{{8}}}^{\circ}=}{p}\)
\(\displaystyle{{\cot{{8}}}^{\circ}=}{{\tan{{82}}}^{\circ}}\)
\(\displaystyle{c}{\quad\text{or}\quad}{8}^{\circ}={r}\)
\(\displaystyle{{\csc{{8}}}^{\circ}=}\frac{{1}}{{{\sin{{8}}}^{\circ}}}\)
\(\displaystyle{{\csc{{8}}}^{\circ}=}\frac{{1}}{{q}}\)
\(\displaystyle{{\sec{{8}}}^{\circ}=}\frac{{1}}{{{\cos{{8}}}^{\circ}}}\)
\(\displaystyle{{\sec{{8}}}^{\circ}=}\frac{{1}}{{p}}\)
\(\displaystyle{{\tan{{8}}}^{\circ}=}\frac{{1}}{{{\cot{{8}}}^{\circ}}}\)
\(\displaystyle{{\tan{{8}}}^{\circ}=}\frac{{1}}{{r}}\)
0

Relevant Questions

asked 2021-03-06
Find an equation of the plane passing through the three points given. P = (2, 0, 0), Q = (0, 4, 0), R = (0, 0, 2)
asked 2020-11-03
Given:
\(\displaystyle\theta={240}^{\circ}\)
Find the value of \(\displaystyle\theta\) in radians (in terms of \(\displaystyle\pi\))
asked 2020-12-28
Find the radius, if
s=38,000cm
\(\displaystyle\theta={45.3}^{\circ}\)
Use the arc length formula.
asked 2021-01-10
\(\displaystyle{\cos{{2}}}\theta=\frac{{28}}{{53}}\)
Find \(\displaystyle{\sin{\theta}}\), if
\(\displaystyle{0}^{\circ}{<}\theta{<}{90}^{\circ}\)
asked 2021-02-26
The minute hand of a clock is 6 inches long and moves from 12 to 4 o'clock. How far does the tip of the minute hand move? Express your answer in terms of \(\displaystyle\pi\) and then round to two decimal places.
asked 2021-02-13
Given a right triangle. One of the angles is \(\displaystyle{20}^{\circ}\). Find the other 2 angles.
asked 2021-02-16
Consider the line represented by the equation 5x + 2y = 10. How is the slope of the line related to values of A, B, and C in standard form Ax + By = C?
asked 2020-11-09
A. Let (X,d) be a metric space. Define a diametr of a ubset A of X and then the diametr of an open ball with center \(\displaystyle{x}_{{0}}\) and rarios r>0.
B. Use (A) to show that every covergence sequnce in (X,d) is bounded.
asked 2020-12-06
Micheal came up with a design of a rectangular patio that is 25 ft by 40 ft., and that is surrounded by a terraced strip of uniform width planted with small trees and shrubs. If the A of this terraced strip is 504 ft^2, find the width (x) of the strip.
asked 2021-02-21
Express \(\displaystyle{\tan{\theta}}\) in terms of \(\displaystyle{\sin{\theta}}\).
...