Answer:
(7, 3)
Step-by-step explanation:
get rid of the y by adding:
x=-2
+x=16
then add the equalities:
2x=14
divide by 2:
x=7
then subsitute the x in to find y!
7+3y=16
3y=16-7
3y=9
y=3
First, tan(<em>θ</em>) = sin(<em>θ</em>) / cos(<em>θ</em>), so if cos(<em>θ</em>) = 3/5 > 0 and tan(<em>θ</em>) < 0, then it follows that sin(<em>θ</em>) < 0.
Recall the Pythagorean identity:
sin²(<em>θ</em>) + cos²(<em>θ</em>) = 1
Then
sin(<em>θ</em>) = -√(1 - cos²(<em>θ</em>)) = -4/5
and so
tan(<em>θ</em>) = (-4/5) / (3/5) = -4/3
The remaining trig ratios are just reciprocals of the ones found already:
sec(<em>θ</em>) = 1/cos(<em>θ</em>) = 5/3
csc(<em>θ</em>) = 1/sin(<em>θ</em>) = -5/4
cot(<em>θ</em>) = 1/tan(<em>θ</em>) = -3/4
Answer:
See below in bold.
Step-by-step explanation:
(1) cosec ( x + 10) = 3
Now cosec x = 1/sin x so
1 / sin (x + 10) = 3
3 sin (x + 10) = 1
sin (x + 10) = 1/3
x + 10 = 19.47 , 160.53 degrees
x = 9.47, 150.53 degrees.
(ii) cot (x - 30) =0.45
cot (x - 30)= 1 /tan (x- 30) so we have
tan (x - 30) = 1 / 0.45 = 2.2222
x - 30 = 65.77 degrees
x = 95.77 degrees.
Answer:
70
Step-by-step explanation:
the red lines mean the two sides are equal
so its an isosceles triangle meaning the two angles other than the 40° one are equal
the inner angles of a triangle must add up to 180
so 180-40 = 2x
140 = 2x
x = 140/2 = 70
Answer:
the interest is 960.
Step-by-step explanation:
the formula: I=prt i=interest p= pricipal [the money you start with]
r= rate t= time
I=? I= 800 (0.02) (10)
P= $800 I= 160+ 800 {because $160 is added}
R= 2% --> 0.02 [as a decimal] I= $960
T= 10 years