Yes, that's a shortcut often used for powers of functions.
Please note that for the special case of function to the power minus 1 of x there is a different definition - it is usually taken to mean the inverse function. So, if you want to write the reciprocal of a function, you have to express it in a different way.
(1 - csc2x)/(sinx*cotx) = -cot2x/sinxcotx = -cotx/sinx = -(cosx/sinx)/sinx = -cosx/sin2x = -cosx/(1-cos2x) = cosx/(cos2x - 1)
(-1)2=1 all squared numbers turn out positive and 12=1 (-1)2=1 all squared numbers turn out positive and 12=1
Please Excuse My Dear Aunt Sally... PEMDAS P = parenthesis E = Exponent M = Multiply D = Divide A = Add S = Subtract In other words, order of operation as it is know in mathematics. So coming full circle to your question, parenthesis are typically reserved in equations force a portion of a calcuation to be completed before another, i.e. 1+2*3=7, while (1+2)*3=9. In the second equation, parenthesis are inserted to make sure the addtion is completed prior to the multipication. However, in the question you pose the answer would be the same. (11)^x = 11^x All that said, if the parenthesis in question in in a line of software code, most programs will only connect the term immediately before the carrot "^" as being raised to the power. So a program would read 11^x as 1*1^x instead of (11)^x, thus the need for the parenthesis.
X=60 how did you get that? could you show all the steps?
When you square a number, the final digit is the final digit of the 'one's' number squared. Since the only single digit numbers squared which ends in 6 are 4 and 6, the answer is either 4 or 6 (a calculator tells me it is 6) 0 squared is 0. All numbers ending in 0 when squared will end in 0. 1 squared is 1. All numbers ending in 1 when squared will also end in 1. 2 squared is 4. All numbers ending in 2 when squared will end in 4. 3 squared is 9. All numbers ending in 3 when squared will end in 9. 4 squared is 16. All numbers ending in 4 when squared will end in 6. 5 squared is 25. All numbers ending in 5 when squared will end in 5. 6 squared is 36. All numbers ending in 6 when squared will end in 6. 7 squared is 49. All numbers ending in 7 when squared will end in 9. 8 squared is 64. All numbers ending in 8 when squared will end in 4. 9 squared is 81. All numbers ending in 9 when squared will end in 1. So square numbers can only end with 0, 1, 4, 5, 6 or 9.
(1 - csc2x)/(sinx*cotx) = -cot2x/sinxcotx = -cotx/sinx = -(cosx/sinx)/sinx = -cosx/sin2x = -cosx/(1-cos2x) = cosx/(cos2x - 1)
(-1)2=1 all squared numbers turn out positive and 12=1 (-1)2=1 all squared numbers turn out positive and 12=1
a=64 b=8 (x+16x+64)=(x+8)^2
It lets you multiply all the numbers in the parenthesis from the number that is outside the parenthesis.
Please Excuse My Dear Aunt Sally... PEMDAS P = parenthesis E = Exponent M = Multiply D = Divide A = Add S = Subtract In other words, order of operation as it is know in mathematics. So coming full circle to your question, parenthesis are typically reserved in equations force a portion of a calcuation to be completed before another, i.e. 1+2*3=7, while (1+2)*3=9. In the second equation, parenthesis are inserted to make sure the addtion is completed prior to the multipication. However, in the question you pose the answer would be the same. (11)^x = 11^x All that said, if the parenthesis in question in in a line of software code, most programs will only connect the term immediately before the carrot "^" as being raised to the power. So a program would read 11^x as 1*1^x instead of (11)^x, thus the need for the parenthesis.
parenthesis means that you do all that you have to get rid of them first
X=60 how did you get that? could you show all the steps?
When you square a number, the final digit is the final digit of the 'one's' number squared. Since the only single digit numbers squared which ends in 6 are 4 and 6, the answer is either 4 or 6 (a calculator tells me it is 6) 0 squared is 0. All numbers ending in 0 when squared will end in 0. 1 squared is 1. All numbers ending in 1 when squared will also end in 1. 2 squared is 4. All numbers ending in 2 when squared will end in 4. 3 squared is 9. All numbers ending in 3 when squared will end in 9. 4 squared is 16. All numbers ending in 4 when squared will end in 6. 5 squared is 25. All numbers ending in 5 when squared will end in 5. 6 squared is 36. All numbers ending in 6 when squared will end in 6. 7 squared is 49. All numbers ending in 7 when squared will end in 9. 8 squared is 64. All numbers ending in 8 when squared will end in 4. 9 squared is 81. All numbers ending in 9 when squared will end in 1. So square numbers can only end with 0, 1, 4, 5, 6 or 9.
The rules of PEMDAS are 1. Parenthesis anything in them you do first. 2. Exponents those little numbers next to the number telling you to multiply the number by itself a certain number of times 3. Multiplication and Division whichever comes first and 4. Addition and Subtraction whichever comes first. If there is an exponent next to parenthesis but there is no number that means the answer to the parenthesis has to be the thing that the exponent is next to. All of the rules apply inside of the parenthesis as well. If there is a number next to the parenthesis not followed by a symbol multiply the answer to the parenthesis by that number.
For simplicity's sake, X represent theta. This is the original problem: sin2x+ cosX = cos2X + sinX This handy-dandy property is key for all you trig fanatics: sin2x+ cos2x = 1 With this basic property, you can figure out that sin2 x=1-cos2x and cos2x= 1-sin2x So we can change the original problem to: 1-cos2x+cosx = 1-sin2X + sinX -cos2x + cosx =-sin2x + sinX Basic logic tells you that one of two things are happening. sin2x is equal to sinx AND cos2x is equal to cosx. The only two numbers that are the same squared as they are to the first power are 1 and 0. X could equal 0, which has a cosine of 1 and a sine of 0, or it could equal pi/2, which has a cosine of 0 and a sine of 1. The other possibility whatever x (or theta) is, it's sine is equal to its cosine. This happens twice on the unit circle, once at pi/4 and once at 5pi/4. If you're solving for all possible values for x and not just a set range on the unit circle, then the final solution is: x=0+2pin x=pi/2+2pin x= pi/4 +2pin x=5pi/4+2pin (note that n is a variable)
1,4,9,16,25,36,49,64,81,100,121,144,169,196,225
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