Emily has been commissioned to create a pastry design for a college math class that can serve the dual purpose of being a tastry treat as well as a matching quiz for the students to test their knowledge of trigonometric identities. To assist with the design process, Emily has received a list of mathematical expressions involving trigonometric identies from the professor. However, as she is creating the treats, she realizes that she is missing the solution key! Since it is too late in the day for her to reach out to the professor, Emily asks you for help with simplifying some of these identities. 3 2 Use basic identities to help Emily to simplify sin\" + cos z sin x. Enclose arguments of functions in parentheses. For example, sin (2z). Remember that writing sin(x) to the fourth power as sin4 (z) is just a mathematical shorthand. You should write it as (sin (:c))4 which is what Mobius expects. 3 sin z + cos? zsinz = BB Emily has been asked to create a game using cupcakes for a convention. The organizers have given her an interesting challenge: they want her to decorate cupcakes that incorporate math problems! Specifically, they would like her to decorate cupcakes that use trigonometry formulas. Emily decides to create cupcakes that involve the trigonometric identities where the event attendees will be challenged to match up the expression on one cupcake with the correct rewritten answer displayed on another cupcake. One of the problems she needs to solve involves rewriting sin (:v + ) in terms of sin and cos x. 6 How would Emily rewrite this for the matching cupcake in the game? Enclose arguments of functions in parentheses. For example, sin (2z). sin (2 + 57 ) = BB Emily loves experimenting with new ingredients and techniques to create delicious desserts. One day, while preparing for a competition, she decides to use a unique gas to create a stunning effect in her pastry. She uses oxygen gas to create a beautiful blue flame on top of her dessert. Emily remembers learning about the ideal gas law in school. which states that the volume V of an ideal gas varies directly with the temperature T" and inversely with the pressure P. She realizes that this law can help her determine the pressure of the oxygen gas in her cylinder under different conditions. Currently, the oxygen gas in her cylinder is at a temperature of 310 degrees K and a pressure of 18 atmospheres in a volume of 120 liters. Emily wants to decrease the volume to 95 liters and increase the temperature to 320 degrees K, but she needs to know the new pressure to make sure the gas will still work for her dessert display. Round your answer to two decimal places. The pressure is | Numbes atmospheres