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:
Increase (A)
Step-by-step explanation:
If the common ratio is greater than 1, that means the y-value increases as the x-value increases.
If the common ratio is 1, that means the y-value stays the same as the x-value increases.
If the common ratio is between 0 and 1, that means the y-value decreases and approaches 0 ad the x-value increases.
Because the common ratio is greater than 1, the answer is A, increases
Answer:what is the fraction?
Step-by-step explanation:
Answer: 6
Step-by-step explanation: 1. 5c-c= 4c. The equation would then be 4c+10=34.
2. From there, you subtract 10 from both sides of the equation. By doing this, you have the variable and the nonvariable on separate sides of the equation.
3. After doing that, you should have 4c=24. To get the variable by itself, divide both sides by 4. 4c/4 is c and 24/4 is 6.
The final answer is 6. Hope this helped you:)
Answer:
The first step is to find a number that when subtracted from 2 gives you 2.
Step-by-step explanation:
The algebraic part of this problem would be to add the -2 (adding 2 to both sides) to both sides, so
first x-2=2, then x-2(+2)=2(+2) which would give us,
x=4
*note: the parenthesis are just to show that we are adding the 2, to make it more understandable.
