1 + tan ² Ф=sec²Ф
1+(12/5)²=sec²Ф
169/25=sec² Ф
sec Ф=⁺₋√(169/25)=⁺₋13/5
sec Ф=1/cos Ф ⇒cosФ=1/sec Ф
cos Ф>0 ⇔ sec Ф>0 ⇔ sec Ф=+ 13/5
cos Ф=1/secФ
cos Ф=1 / 13/5=5/13
we can calculate the sin Ф, with this method.
sin²Ф + cos²Ф=1 ⇒ sin Ф=⁺₋√(1-cos² Ф)
sin Ф=⁺₋√[1-(5/13)²]=⁺₋12/13
like cos Ф>0 and tan Ф>0 ⇒ sin Ф>0 ⇒sin Ф=12/13
answer: d.12/13
other method
tan Ф=sin Ф / cos Ф
12/5=sin Ф / 5/13
sin Ф=(12/5)*(5/13)=12/13
answer: d.12/13
Because it's decreasing, you use the formula (1-x/100)y with x the percentage decreased which is here 40, and y the number decreased which is here 90
So we get
(1-40/100) * 90
(100/100 - 40/100) * 90
60/100 * 90
5400/100
54
So 90 decreased by 40% is 54
Hope this Helps :)
I wrote it out on paper and uploaded the answer for you. Let me know if you have any questions.
Answer:
The answers are below
Step-by-step explanation:
The greater sign is > and the less then symbol is <
Using the red arrows on the number line, you can tell which one is bigger or less. The dot is colored in so it has to have a line under it. So for the first one (top, left), The red arrow is pointing to the right side meaning x is bigger than 3. Therefore x ≥ 3.
In the next one (top, right) the arrow is pointing to the negative side so that one must be less than 3. The dot is also colored in meaning it is: x ≤ 3
In the next one (bottom, left) the arrow is pointing to the right, the dot not colored in, so it has no line. Therefore it is x > 3
Last one (bottom right) the arrow is pointing left, dot is white meaning that the answer is x < 3
If you're wondering what the open dots and closed dots mean:
An open dot is used to show that the ray's endpoint is not a component of the solution when the inequality is "strict" ( < or >).
A closed dot is used to denote that the endpoint is a component of the solution for the other types of inequalities (≥ and ≤ ).
