Answer:
Step-by-step explanation:
Given the expression cosec (x) = 4 and tan(x)< 0
since cosec x = 1/sinx
1/sinx = 4
sinx = 1/4
From SOH, CAH TOA
sinθ = opposite/hypotenuse
from sinx = 1/4
opposite = 1 and hypotenuse = 4
to get the adjacent, we will use the Pythagoras theorem
adj² = 4²-1²
adj² = 16-1
adj ²= 15
adj = √15
cosx = adj/hyp = √15/4
tanx = opposite/adjacent = 1/√15
since tan < 0, then tanx = -1/√15
From double angle formula;
sin2x = 2sinxcosx
sin2x = 2(1/4)(√15/4)
sin2x = 2√15/16
sin2x = √15/8
for cos2x;
cos2x = 1-2sin²x
cos2x = 1-2(1/4)²
cos2x = 1-2(1/16)
cos2x= 1-1/8
cos2x = 7/8
for tan2x;
tan2x = tanx + tanx/1-tan²x
tan2x = 2tanx/1-tan²x
tan2x = 2(-1/√15)/1-(-1/√15)²
tan2x = (-2/√15)/(1-1/15)
tan2x = (-2/√15)/(14/15)
tan2x = -2/√15 * 15/14
tan2x = -30/14√15
tan2x = -30/7√15
rationalize
tan2x = -30/7√15 * √15/√15
tan2x = -30√15/7*15
tan2x = -2√15/7
Answer:
(d) (7, -5)
Step-by-step explanation:
The x-coordinate is listed first in an ordered pair. It is found on the horizontal scale. The point is on the grid line halfway between 6 and 8, so is presumed to have an x-coordinate of 7.
The y-coordinate is listed second in an ordered pair. It is found on the vertical scale. The point is on the grid line halfway between -4 and -6, so is presumed to have a y-coordinate of -5.
The coordinates of point A are (x, y) = (7, -5).
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<em>Additional comment</em>
As in the case here, you will often run across graphs that don't have markings on every grid line You are expected to be able to figure out the value of a grid line based on the spacing of the marked lines.
It is a good idea to get familiar with reading coordinates of a point on a graph, as you will be doing it a lot.
The odd number before 149652 is 149651
Answer:
<u>x = 25</u>
Step-by-step explanation:
<u>Solving</u>
- ∠CAD = 1/2 ∡ CD
- 180° - 90° - (2x)° = 1/2 (80°)
- 2x = 90° - 40° = 50°
- <u>x = 25</u>
