First of all, you know that a fraction is smaller than 1 if the top number is smaller than the bottom. It works both ways, meaning that if the top number is larger than the bottom number, the fraction is greater than 1.
So, for example, a fraction less than 1 can be expressed as
(x-1)/x
because the top number is smaller than the bottom number.
The reciprocal can be found by flipping the top and the bottom, so the reciprocal is
x/(x-1)
x is always greater than x-1, so in the reciprocal, the top number will be larger than the bottom number. That means it will always be greater than 1.
Hope this helps!
(Sorry if this is confusing)
+ 1 = 3
First, multiply both sides by 3. / Your problem should look like: x + 3 = 9.
Second, subtract 3 from both sides. / Your problem should look like: x = 9 - 3.
Third, simplify 9 - 3 to 6. / Your problem should look like:
x = 6, which is your answer.
Answer:
Step-by-step explanation:
3x + 4(x - 8) - x = 3/5 (10x + 15)
3x + 4x - 32 - x = 3(2x + 3)
6x - 32 = 6x + 9
This is what I did. I'm not sure that this problem has a solution
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
