Recall the pythagorean identity sin2(theta) + cos2(theta) = 1, where theta is any real number.
a. find sin(x), given cos(x) = 35, for − / 2 < x < 0.

-4/5

Step-by-step explanation:

If ABC is a right triangle having ∠B= 90° and the sides AB, BC, and CA are respectively the perpendicular, the base, and the hypotenuse.

Now, if ∠C is equal to Ф, then Sin Ф =Perpendicular / Hypotenuse = AB/CA and Cos Ф =Base / hypotenuse = BC/CA

Hence, Sin²Ф + Cos²Ф = AB²/CA² + BC²/CA² =(AB²+BC²)/ CA² = CA² /CA² =1 {Using Pythagorean Theorem, AB² +BC² =CA² i.e (Perpendicular)² +(Base)² = (Hypotenuse)²}

Now, if Cosx = 3/5 where -π/2 < x <0 i.e. the value of x lies in 4th quadrant, where Sinx will be negative then  

Sin²x= 1-Cos²x =1- (3/5)² =(4/5)²

⇒ Sin x = -4/5 (Answer)

step-by-step explanation:

f(x)=2x^2 -1 

translation is a function transformation that transform the function in a way of translating. by translating the function its graph is moved  up an down. moving the function f(x) 2 units to the left will be the new function g(x) with the equation: g(x)=f(x+2)=2(x+2)^2 -1

the most boring ever written

step-by-step explanation:

i am writing something. yes, i plan to make it the most boring thing ever written. i go to the store. a car is parked. many cars are parked or moving. some are blue. some are tan. they have windows. in the store, there are items for sale. these include such things as soap, detergent, magazines, and lettuce. you can enhance your life with these products. soap can be used for bathing, be it in a bathtub or in a shower. apply the soap to your body and rinse. detergent is used to wash clothes. place your dirty clothes into a washing machine and add some detergent as directed on the box. select the appropriate settings on your washing machine and you should be ready to begin. magazines are stapled reading material made with glossy paper, and they cover a wide variety of topics, ranging from news and politics to business and stock market information. some magazines are concerned with more recreational topics, like sports card collecting or different kinds of hairstyles. lettuce is a vegetable.